From a technical point of view if you make a donation to a 501(c)(3) organization with the stipulation that it be used for Joe Smith Jr. you are not entitled to a deduction.
Realistically, an unrelated business can make a small payment (less then $500) to a player and deduct in a number of different ways, promotion, marketing etc... and most IRS agents won't care. However, if the business wants to make a large payment it may run into 1099 and other pratical reporting issues. i.e. Most IRS agents won't ask about a $200 promotion deduction but will ask to see the 1099 the business issued if its a $1,000 payment.
Many travel teams will provide players with form letters requesting financial aid etc. to help kids find "sponsors" for their trip.
fyi most Little League Babe Ruth etc. organizations are tax exempt as "educational"
. Many travel teams are NOT 501(c)(3) organizations because they would become subject to public oversight by the state attorney general, would have some of their financial records open to the public and would be "owned" by the public.