I would go with the second one. It would be better.
Without the "Unfortunately" part, "Spor için hiç vaktim yok" might also mean you don't care about the sports so as to spare time for it.
The second one however, "spor için hiç vaktim olmuyor", shows how willing you are to play sports but you don't have free time to do it.
If I were you, I would say; "Maalesef spor için bu sıralar hiç vaktim olmuyor."