First food of choice for rabbits has to be grass.  Rabbits have evolved to eat large amounts of relatively low nutrition foods (such as grass and dried grass - also known as hay) and anything that's rich and concentrated WILL give them digestion problems.  So put a good double fistful of green grass (or other greens, see further on below) and a similar amount of hay on your rabbit's daily diet.  Such feed is high in fibre and keeps the rabbit digestive system percolating along nicely.

Along with that high percentage of fibre, a small amount of concentrated energy is permissible. Be careful - rabbits like all other species recognise a high value food and will tend to eat that rather than the poorer feeds.  But letting them have their way on such foods may well kill them or make them very ill.  High energy foods include things like apples, raisins, carrots, bananas, strawberries, and similar fruits and vegetables.

The second trouble-free feed for rabbits is the pelleted rabbit food that's sold at pet and stock feed stores.  It's formulated to be high fibre, just the right amount of protein, and trace elements.  Rabbits are very much creatures of habit so if you feed only pellets they would probably be quite happy to eat pellets every day.  But I recommend the additional feeds because they provide interest and a chance to bond with your rabbit.  

Some green leafy vegetables such as kale and silver beet and spinach are quite high in calcium  and should be a part of the weekly diet of rabbits.  These are a bit tricky to figure out, so ask your local rabbit club or pet store about vegetables in your area.  For instance, the basic iceberg salad lettuce is water and cellulose, and it will give your rabbit the scours (runny poop) and that can quickly dehydrate and kill a rabbit.  Yet thick Cos (also known as Romaine) or Oakleaf or Mignonette lettuce will not have that effect.  I'll describe how rabbits cope with new foods and you can then apply the same principles to foods you try with your rabbits. 

Also, rabbits need something to chew on, for the sake of keeping their teeth at the right length.  For this, you can introduce wood and hard foods like the occasional wheat grains etc.  Note that many kinds of wood are poisonous, so as for everything, follow the instructins below.  Most importantly, make sure the rabbit has clean water all the time.  Because their digestive systems are so rapid, rabbits need reliable water supplies.  

Rabbits have a strategy when they come across a new plant.  I'll describe it to you, and you'll easily see how to apply it to your rabbit, your situation.  

Firstly, you need to know that rabbits produce two kinds of poop.  The little dry ball bearings, they are wastes.  Rabbits will still often pick these up and eat them, I'll get to the reason in a moment.  The other kind of poop looks like smaller ball bearings all stuck together like a mucousy bunch of grapes.  Rabbit MUST re-ingest these so-called "cecal" pellets, because their digestive systems are so unique.  The cecals contain gut bacteria, and the gut bacteria are specific and unique to the rabbit and the types of food it has 'learned" to digest.  Because their digestive systems are so fast, these bacteria would mostly be flushed out of the stomach by peristaltic action.  And therefore, rabbits need to continuously "re-infect" their gut with the bacteria, otherwise they will die of starvation while eating as much or even more than normal.  Accept that a lot of subtle rabbit interaction and internal action occur through the mediums of fecal and cecal matter.

But this also leads to a situation where a rabbit can "learn" about a new food and digest it.  In this, I've observed that both kinds of pellets seem to be important.  A rabbit comes across a new plant in its territory, and performs a series of actions that all mine have shown. They will first nibble a merest mouthful of the food, and then move away from it to prevent them from accidentally eating more of it.  They'll not go back there for at least several hours, sometimes not for a whole day.  This is to establish if the food is poisonous to the rabbit or not.  Hopefully a single mouthful won't be enough to kill the rabbit, but it might make it ill or cause it pain or distress.  In that case, the rabbit will associate that plant with pain and distress and won't eat it again.  Meanwhile, its fecal ball bearings have had time to get through the gut and be dropped on the ground.  The scent of these will have the smell of the plant, and the smell of the gastric disorder that the plant caused.  Other rabbits, coming across these pellets, will be able to know that plant and its effect, and avoid it just like the "guinea pig" rabbit will.

If the rabbit finds that it isn't poisoned, it will go back for a few more mouthfuls, again not much but a bit more than before.  This now has two effects, one is that the rabbit's gut bacteria will start to adapt to the new food, and the second is to tell the rabbit if higher quantities maybe have a toxic effect where one mouthful didn't.  Again, both it and its herdmates will now be able to pick up fecal pellets and "know" about this new food source, and I suspect that some gut bacteria may also be passed between rabbits in these fecal pellets.  But after this, the plant is considered a food source and rabbits will now graze on it along with their other forage.

So - to try out a new food with your rabbit, first offer just a few bites of it.  If the rabbit outright refuses it, and you're pretty sure it shouldn't be harmful, you can offer it again the next few days. At some stage, if the rabbit takes a few bites, then take the rest out of their reach, and let them digest it for a day, offer a bit more the following day, remove the rest, and finally, you can give it to the rabbit as freely as you consider will be good for the rabbit. 

Many kinds of wood are suitable for rabbits to chew on - untreated pine can be used but isn't really recommended (which cuts out those ridiculous garishly coloured wooden chew things that pet shops sell - avoid those if you can) and better is apple wood, if you can get it.  I believe raspberry old wood may be okay, and I know Syzigium (Australian Lilly Pilly) wood is, but you need to ask locally of your pet shops and rabbit clubs.  Many woods are actually poisonous, so be very careful.  Use the above regime for testing it - one nibble and remove the chew branch, and observe.  

Grass and hay are always good, oaten hay is not as good as lucerne (alfa alfa) hay, and timothy hay and meadow hay are also good.  If you have a lawn, let your rabbit forage around by itself, fresh grass is a favoured staple for rabbits.  Pellets - ask your local rabbit sources which are the best, look for relatively high fibre content.  A fair assessment of quantity might be that a dwarf lop rabbit would eat 1/2 a cup of pellets and a double handful each of hay and grass per day, plus other foods as below.  

With regard to pellets:  take a few pellets and sprinkle them with water.  Once they's swollen up on a few drops per pellet, add more water.  Observe, discuss.  The pellets can swell to three or four times their dry size - on a rabbit with normal water intake, they will expand that much, and turn fluffy and soft in the process, and easy to eliminate.  In a rabbit with restricted water intake, they will swell to only half that size, remaining quite hard and difficult to pass along the gut.  The rabbit will also feel hungrier because its gut isn't as full, and therefore eat more pellets.  Can you say "lump of something like concrete lodged in gut and blocking it?"

Cabbages in small quantities, most brassicas (cauliflower, broccoli, brussels sprouts) in small quantities.  Kale, silver beet, spinach, many Chinese leafy greens - in slightly more quantity.  (here we're talking a half a cupful of shredded cabbage or one cupful of shredded kale.) Carrots, apples, banana, grapes, strawberries, sweet peas and peas in pods etc - half a cupful at most.  

Things like avocado, corn, beans, high protein vegetables that will cause scouring.

Cubes of bread, raisins, a few grains of wheat, a corner of a plain cracker biscuit.  Much of this food is too unbalanced in terms of fibre/protein./sugars and and will definitely give buns the runs.  

Mix it up - make one day a kale day, another day grass, then a dry feeds day, etc.  Also, feed your rabbit in the evening for best effect, as rabbits graze in the evening and night.  Feed snacks and treats earlier in the day, to differentiate rewards from the daily feeding.