I don't know what the reason is you're looking for vegan ideas, but just in case you're making some for someone else who is vegan, I thought I would point out that most vegans don't do wool. If that's the case, the felted eggs may not be a good idea. If you put that in just because you don't want so many eggs to eat, my apologies.
We made some homemade baking clay eggs to paint a few years ago that came out alright, some of them split during the baking, though. I think they were just too big to be solid. We use this recipe here now for our baking clay and haven't had it split at all, but we haven't made eggs with it yet, so no guarantees!
This year we're painting paper mache eggs. You can either wad up newspaper / paper towel / scrap paper / etc. and put a little masking tape around it to hold an egg shape, or if you already have plastic eggs to use that would be even easier. Just mix some water into white glue (like 3/4 glue, 1/4 water,) dip newspaper / paper towel / newsprint strips into it, wrap, and let dry. It doesn't need to be very thick and should dry over night.
You can also find packs of paper mache eggs for painting at most craft stores for pretty cheap if you want to go as easy as possible.