Both are correct! :) "When will you be available?" sounds longer and little more formal than "When are you available?" (<--This one is more casual.)

Both of these sentences are correct. They have almost the same meaning, and they can be used interchangeably in most contexts. When will you be available? - suggests some time in the future or far future. (tomorrow or later) When are you available? - suggests some time in the near future. (today/tomorrow)