I have a tried and true cake recipe that I use for all my cakes with just a little adjustment to suit tastes and flavors. Carrot cake however is eluding me! It's such a moist cake so it doesn't lend it's self to much decorating. A customer has asked for a carrot cake shaped into a solo cup! Help!

Really?  I never have a problem decorating carrot cake.  My carrot cakes are really dense and moist, but not brick-like.  Most carrot cake recipes are basically the same in my opinion.  I don't put coconut or pineapple in mine.  Mine is generally just carrots and sometimes I throw in toasted pecans or walnuts.  Can you post the recipe you're using?  There are good recipes on this site, or you could try Allrecipes.  I think one on here I tried was called Carrot Cake or Banana Cake, because it could be used for either.