It is important to find the root cause why they don't want to participate. My daughter excluded herself from some activities she would have enjoyed and been good at simply because the crowd she was hanging with didn't do it, or because there was someone in it whom she didn't like. Some kids dream of doing something but they are terrified of failure or ridicule. They are already damaged, and it is very important to find a safe supportive activity where the program builds success into it and there is no way they can fail or be ridiculed. It is equally important to find why kids DO want to participate. If they are doing it for any reason besides really enjoying it (such as to please Dad or Mom) they should probably not be encouraged.
If your kid is dragging their feet, take a look at the program and see how the coach/facilitator treats the non star kids. If he/she is only interested in the star kids and your kid isn't one, your kid probably won't gain much from it anyway. You can look for a different league or (I know this is really old fashioned) just facilitate your kid doing fun activities with friends that they pick. Don't underestimate how badly an obnoxious little jerk in any group who isn't roundly put in his place (i.e. asked to leave) can spoil the experience for everyone.
I think it is important for every kid to do one or two group things that they really enjoy. It's just harder to find a fit for some than for others. And talk to them and find out what they are gaining from it.