Brian Mailman, OUcooking.org Columnist - Slow Food in the Fast Lane says:
Any bread recipe can be formed into a hamburger bun shape and with that in mind the entire lexicon opens up. I would suggest a challah, 'cuz of the cake-like texture that I think you're wanting. Onion rolls or Kaiser rolls are also a good choice.
What milk does in a bread recipe is affect texture. It's what gives the even, close-grained "crumb" and 'swhy I recommended challah buns, above. While you most certainly can sub in non-dairy milks, they aren't necessary and don't add anything more than water would. You can substitute margarine 1:1 (one for one) with any butter, but do not use a "spread," or soft tub-type margarine. If using oil, cut back to 2/3 the amount called for; margarine is 1/3 water.
Tamar Ansh, OUcooking.org Columnist - Nutritious and Delicious says:
My experience, for the most part, with converting recipes that are made dairy, into non dairy use is that almost universally you can use margarine instead of butter. For health reasons, I personally always try to see if I can use canola oil instead, and most of the time, it does work. Especially when you are making any kind of bread dough, you can usually take out all margarine and put in the same amount of oil. However, when you do it the first time around, you can try a half/ half idea, ie put in half the amount of butter using margarine and the other half, oil. See how you like it and write it down for the next time you make that recipe. Then decide if you want to experiment further and use only oil.
For buns, if I really want a milk taste, I use soy milk. It's best to use one that is not overly sweet. If the recipe calls for a lot of liquid and I'm afraid of it tasting "too soy -ish" then I use half soy milk and half water. When baking I find that this usually works well. In cooking, though, I find that you can detect the soy milk flavor so I've stayed away from large amounts of soy in cooking. I either use water or wine or only small amounts of soy milk for cooking. Rice milk has less of an overpowering taste in cooking, but again, I start off using less and substituting water and only then deciding if I can increase it. I have found that using soy milk in muffins or cakes works nicely and generally comes out well.
That being said, if you don't want to risk it, use water. It can't be bad. After all, challah doughs use only water and they always taste good! Then if you want to "see what happens" the following time, try it with soy. You can then compare.
I'd love to hear what you come up with and if your recipe works great, let us know!
I can post here a recipe for just such a bun that I worked on a while ago, but have not used for a while. I would love for you to try it and tell me back how you liked it. From what I can remember, it came out good, but flatter than I had anticipated (real buns are made in a special bun pan that keeps that round shape we all love so much).
WHOLE WHEAT ROUND BURGER BUNS
Makes 8 buns
1 cup rice or soy milk
½ cup lukewarm water
2 ¼ tsp. / 1 package active dry yeast
1 large egg, room temp, lightly beaten
1 T. light brown sugar
1 tsp. salt
2 T. olive or canola oil
1 & ¾ cups finely ground whole wheat flour (or white flour)
1 & ¾ cups regular whole wheat flour
cornmeal and bran for dipping
Kol tuv and happy baking