I would think that TNT will dominate prime-time tomorrow night (May 29th) with Game 7 of the NBA series between Boston and Miami.
In fact, it will probably be the most watched NBA game ever on cable television and will probably draw more viewers than all of the broadcast networks combined (I'm projecting 10-11 million viewers for TNT and 9-10 million viewers for ABC, CBS, The CW, Fox, and NBC combined) thanks to a made-for-TV storyline (can Boston become the first team in NBA history and only the fifth team in the history of North American professional sports to come back from a 0-3 deficit to win a best-of-seven playoff series?).
Of course, ABC (which will carry the NBA Finals) is rooting for Boston since it's a much larger market than Miami, and furthermore, the Boston Celtics are the NBA's most iconic franchise.
Going back to hockey, TNT will have this year's Stanley Cup Finals. Viewership will probably be significantly lower than last year, given that last year's Finals were on ABC (a broadcast network), whereas TNT is a cable network.
TNT is undoubtedly hoping that a Florida Panthers team that barely made the playoffs will complete their Cinderella playoff run by winning the Stanley Cup. That will probably be the focus of their promotion of the network's first ever Stanley Cup Finals.
BTW, this will be the first time since 1994 (New York Rangers defeating the Vancouver Canucks in seven games) that the entire Stanley Cup Finals will be exclusive to cable television in the United States (ESPN carried the 1994 Finals).