Be professional when applying for sponsorship.
Write a short creative brief for the advertising that sponsoring you will give them. (use google to find what is supposed to be in one), outlining the goals and how their logo and name will be used, in what context and how that is in sync with their image and marketing strategies. One page is enough, half a page can be enough if it is concise.
When companies sponsor someone, it doesn't pay off unless they get real exposure for it, which often means that for every 100 they put into the sponsorship, they have to spend another 100 telling the demograph they are trying to reach that they are in fact sponsoring this cool team called X, that X is a great team and they are using their product to gain some advantage. Note all the NeXus ads in latest issues of PGI.
Let's use the energy drink market for example.
Paintball can be considered to have some cool value among teens and young adults, students between 16 - 24. At least among some parts of the demographic, the one that is trying to not be mainstream, do their own things, are always seeking new and exiting experiences and the gun like things add to the "rebel" image. Paintball can appeal to both girls and boys in that mindset.
Who are the biggest users of energy drinks in your locality ? Odds are it's students, students in the mindset described above. Suggest for your sponsorship the team will model for ads to be published in the local student magazines and posters to be hung in the schools and universities. The fact that you may be students yourselves, even in those schools, add to your value as believeable representatives of the brand. And model fees for photoshoots may be higher than what you are asking for.
So you have to show them that the money spent on sponsoring you and on producing and publishing those ads will be money will generate the exposure to justify the cost.
my best
Gudmann Bragi