I have a couple of friends who can't have dairy for one reason or another. Here's a modified version of my Ultimate Cinnamon Rolls for them:
Non-Dairy Cinnamon Rolls
1 tablespoon yeast
2 tablespoons sugar
2 tablespoons warm water
1 cup warm water
1/2 cup (1 stick) margarine
1-1/2 teaspoons salt
5 cups flour
In a large mixing bowl, dissolve the yeast and the 2 tablespoons sugar in the 2 tablespoons of warm water. Melt the margarine and add it to the cup of warm water.
Add the eggs and the water/butter to the yeast and blend well. Add the salt and the flour and use the dough hook of your mixer to knead the dough at a medium speed for five minutes. The dough should be soft and still sticking to the sides of the bowl. Cover the bowl and put it in a warm area for two hours. (See here for a trick if you don't have a warm spot in your house.)
3/4 cup brown sugar
1 tablespoon cinnamon
1/4 cup (1/2 stick) margarine, room temperature, plus an extra tablespoon for buttering the baking pan
Lavishly grease a 9x13" pan with the extra margarine. Mix the brown sugar and the cinnamon together. Take your nicely risen dough out of its bowl and place it on a well-floured countertop. Roll it out into a large rectangle about a half inch thick. Use a bench scraper or big pancake spatula to make sure it isn't sticking to the countertop. The dough will be floppy and hard to handle; this means it will be tender when baked.
Spread the softened margarine evenly over the dough. Top it with the sugar/cinnamon mixture. Roll up the dough evenly and firmly from one long side to the other. Slice the rolls using an 18-inch length of dental floss: hold the floss tightly, slide it under the roll, and bring the two ends up and across the top of the roll until the dough is sliced through. Place the rolls in the greased pan, cover the pan with a dishtowel, and let the rolls rise somewhere warm for another half hour. In the meantime, preheat the oven to 375 degrees F.
Uncover the rolls and bake them for 20-25 minutes, until they are golden brown on top. While they're baking, make the frosting:
1 cup powdered sugar
1 teaspoon vanilla
2 tablespoons water (plus a bit more, if necessary)
Spread the frosting over the hot rolls. Cool and serve.