A little nervousness is a good thing. Shows you care and you're in tune with the importance of it and the desire to win.
Too much makes you your own worst enemy. Leads to choking, tightness and takes you off your best game.
This is a mental thing so the solution is mental. I think that the best medicine for this problem is PERSPECTIVE. If you are really nervous you need to sit down and reassess things. Put it them into proper perspective.
This begins with trusting and believing in yourself. Not talking about your game. But in what you determine your beliefs are. In other words, is a league tournament really that huge and massively important in life? Is winning or losing that huge? In a way, it's sort of downplaying it in your mind to help relieve the pressure and nervousness about it. However, some nervousness is a good thing. Because pool, competition and these tournaments are a part of your life and something you desire and work hard toward. Have to strike a balance. It's important enough to warrant your highest effort and concentration and care/desire to win, but not to the point that it's life altering. Therefore, extreme nervousness is unjustified.
I've seen people get so nervous as if their life depends on the outcome. A tournament isn't a jury decision or something serious. It's a tournament. Yes, you want it. Yes you want to do your best. You have big expectations for yourself and that's ok. A little anxiety about it isn't a big deal. But you have to trust in yourself. You practiced. You did your preparation. There is no reason why you shouldn't do well or fear a negative outcome or just be too nervous.
I only get nervous when I know I didn't prepare. When I know something is wrong or likely to go wrong. When I've done everything right, I go in confident knowing that I am as well prepared as possible. I accept that. If I lose, well I wasn't good enough even though I put forth my best. I can accept that. What I can't accept is not doing my best and losing. That's a let down.
A final note on all this. Too many players make their pool game far too personal. In other words, they take their performance and the state of their game as a reflection of themselves as a person. It simply isn't like that at all. If you lose, it isn't a shot again your person. People get real down on themselves and mentally mix in performance with other issues psychologically and it makes a mess. Sure, a person's character traits do factor into the game - but there are people who do everything right and don't win. It doesn't make that person a loser or a failure. Remember, the other guy is also preparing and trying to win to. Someone has to win, someone has to lose. It's a GAME. It's about FUN.
The loser and failure is the person that does nothing to put forth their best effort and who doesn't believe in themselves. The real losers are the ones not having any FUN.
That's the only time I've ever been a loser. When I sit back after a defeat and realize that the entire experience was stressful, tense, nervous, negative - I failed. I failed at achieving a fun experience. And fun isn't contingent on winning, although winning does help. And there have been times I've won and won well and did NOT have fun. That too is in my world view a failure.
Life's too short to do things that aren't enjoyable. Just remember why you play. To have fun. Then you can go in there with a clearer mind and not so nervous. You'll play a lot better and it will give you even less reason to be nervous. It's almost like having another weapon in your arsenal.