I've been asked to make a vegan cake. Chocolate cake recipe I have is no problem, fondant is no problem. But, what do I use instead of buttercream that'd work under the fondant? It needs to taste good and work... Anyone has any ideas? Thanks!

You could use a buttercream that uses crisco. Or a chocolate ganache?

ganache has cream, so not vegan.  Shortening based buttercream, sub in a little Earth Balance and use soy milk or water.  Powdered sugar can be a problem, so see how strict the customer is.  

Not if you make vegan ganache....

16 ounces good quality dark dairy-free chocolate, coarsely chopped 1 15-ounce can coconut milk (not lite varieties) 1/2 t. vanilla

Which chocolate brand do you recommend? 

Trader Joe's chocolate chips are dairy free! If you don't have access to those Enjoy Life chocolate bars are awesome, I think you can get them on amazon and probably at a health food store.

Aquafaba Swiss merengue buttercream or IMBC.  Try this https://geekycakes.com/2015/05/08/egg-free-dairy-free-vegan-italian-meringue-buttercream/