Pretty much every major golf equipment company sells personalized golf balls. You may very well have to get permission to have it done, but it would be fairly trivial to order balls from Titleist or Bridgestone or Callaway, or even just cheap off-brand balls. To get them done direct from the company is probably situational and may require a bulk purchase but it's entirely possible to have done. Another example:
http://www.titleist.com/custom-imprinting/
EDIT: It's worth noting, though, that golf balls are almost certainly far more expensive (per unit) than most giveaway items. They might be good for a fundraiser with your team's logos, but probably wouldn't be particularly ideal for competition swag.