How about a Little Ceasar Pizza kit sale? Idk if they need a tax id, I don't see why they would though. We have pretty good success with that one. We do it through the gym and our school does it also and makes out very nicely. At the gym, we also do a geranium sale in the spring and I had quite a bit of success with that one also. The other ones that we do would require tax id, so won't go there.
Chicken BBQ dinners usually go over nicely also, and you could look into whether a VFW Post would like to sponsor the girls. Our local VFW makes all kinds of charitable donations. You just have to submit a letter detailing what the Organization (Team) is about and what the money would be used for (new leos, equipment, meet fees, etc...) and when they have their monthly meeting they'll discuss what organizations they'd like to sponsor.
I've heard of teams that print up Tshirts with sponsor names on the back. Business pay to have their logo printed on the back. That is very profitable, but don't know if businesses will donate if they can't use is as a tax write-off (which they can't do unless your a non-profit organization...you need to have more than a tax id for that and is a pain the rear to do). Might be worth a try though to see if businesses would be willing to for-go the tax write-off.
Good Luck