Your two best bets are:
Val Thorens (part of Les Trois Vallees) in France, which is the heighest resort in Europe (and where I will be from the 19th-26th April this season) - conditions often remain good into May, although the usual problems with some slushy afternoons/icy mornings are possible anywhere in Europe moving through April.
Another excellent bet, also in France, is the Espace Killy (Val d'Isere and Tignes). Tignes would probably be the better bet due to Val d'Isere's village being somewhat lower. As well as a huge amount of high altitude terrain throughout the domain, Tignes additionally has a glacier which is used virtually all year and is a favourite for national ski teams in the autumn.
Whilst it wouldn't be top of the list snow wise anyway, avoid Saalbach-Hinterglemm in Austria that week as the British Universities Championships (and huge holiday) is going on that week - i.e. thousands of drunk British students crammed into a relatively small resort... Although it does apparantly have the best lap-dancing club in skidom (according to a magazine I bought yesterday).