The term tragicomedy is often used to describe a serious play with a happy ending. In the twentieth century, it was most famously used in Samuel Beckett's Waiting for Godot. It fits Stoppard's play, not because it has a happy ending, but because it more or less announces itself as a tragedy in the title (we know the two main characters will die the entire play), but the entire play is full of comic elements. In other words, their fate is pre-determined but they have fun goofing around on their way to it. Moreover, since Ros and Guil disappear, it's slightly unclear whether or not they actually die or if this is just a stage death. Guil, in particular, seems to have a hint of the fact that the play he stars in will perform again the next night when he says, "we'll know better next time" (3.347).
If you have time, check out the "Author's Note" in one of the early editions of the play. You can find it on Google books. They don't print it in more recent editions, but Stoppard has an enlightening comment in it that has to do with genre. He says, quite straightforwardly, "My intention was comic, and if the play has not turned out funny I would have considered that I had failed. Quite a lot of solemn and scholarly stuff has been written about it, which is fine and flattering, but it is worth bearing in mind that among the productions staged all over the world, two were comparative failures, and both of these took the play very seriously indeed." The more time you spend with the play, the more tempting it is to talk about it very seriously, but Stoppard reminds us that one must not forget to laugh. At the same time, remember that many true things are said in jest.