Speak with your coach and team captains about enforcing a team pledge of kindness where everyone commits to doing one act of kindness a day for the length of the season.
With their support, introduce this idea to your teammates and get them excited about it. There are so many simple kind things people can do, to do one a day really isn't a huge commitment. Encourage your teammates to hold the door open for someone, pick up litter, buy someone's lunch, reach out to the new kid, say hi to someone in the hallway, or thank a teacher. Get creative! See who can do the most acts of kindness in one day.
As your team tackles this challenge together they will become closer. Teammates will start carrying this attitude with them in competition, too--you don't have to be mean to win.
Hold a competition and see who can do the most acts of kindness in one day. Or do one really big act of kindness as a team--participate in a fund-raising game for a local charity. Build a house with Habitat For Humanity as a team. After every Saturday morning practice go and get bagels and bring them to a local homeless shelter. Make this a written pledge and have each teammate and coach sign it. Frame it and hang it in the locker room to remind everyone of their commitment to kindness.
This doesn't need to be a formal pledge; nor does the whole team have to participate. Start by setting an example yourself. Pick up the water bottles rather than leaving them for the manager to collect and refill. If you are sitting the bench or out injured, offer to keep the stats of the game. Bring snacks for the team to eat after the game. Share with the opposing team as well. Thank the opposing team for playing, whether you won or lost.
Some other ideas for team building on your sports team.