"They have gray skin, orange eyes with gray irises (according to Vriska, these fill in with the troll’s blood pigment as they age, this has been shown with the Condesce, but Sollux and the Ψiioniic are an exception in both regards), pointed teeth, yellow nails, black lips, and black hair.” -source
So, unfortunately, no. Troll’s canonly have yellow nails. However, don’t let that stop you! You can make their nails any color you wish, I’ve seen quite a few cosplayers with black nails.