One of the athletes that trains at my facility has qualified for a national tournament. The athlete is short on $$ for his registration fees is it possible for my business to sponsor him by paying for any or all of event if said athlete is to wear items that advertise for my business?
Yes, you would deduct this as an advertising expense.
You may deduct expenses for advertising your business. It's important to note that these must be ordinary and reasonable expenses for advertising.
Below is from IRS web site: https://www.irs.gov/publications/p535/ch11.html