The only "sponsorships" you'll get is wholesale priced gear from the pb industry. Forget the pb industry, it is a waste of time... theirs and yours.
Local businesses do like write-offs for charity and non-profits. There is no business positives for them to sponsor uniforms or entry fees for pee wee football and little league baseball except that they can boast to the community that they care.
Be very careful how you approach business owners for money. If you come across the wrong way, you will be permanently despised. The best thing that I can think of that is proven is to ask a local business if they need help distributing coupons. Believe it or not, it is very costly to distribute them if you hire a company to do it for you. It is an insane amount of time for a small business owner to do it themselves.
That is one proven method that I have had the kids that I coached do and it has paid off pretty well for them. Key in begging for money is asking a business owner what they need. If you can provide that service cheaper and give the same results as a professional, that owner would be a fool not to use you. Often times, you have to keep casting your lure before you finally score.
In terms of begging for money, you will spend a ton of time initially, persistence is the key.
This now concludes my lecture on begging for money.