You're never legally required to use the trademark symbol in an editorial/news context. As someone else said, just capitalize as you would any proper noun. (By the way, no, you don't have to capitalize every letter, a la SPAM or USA TODAY, regardless of what the product does with its own name.)
If you are writing promotional copy -- I think you said it was for a contest -- that's a gray area. If you're doing a news story about a contest your paper is sponsoring, no, you don't need the TM symbol or a circled-R (registered trademark) or an SM (service mark) or a circled-C (copyright) or anything else some corporation may insist upon. But if you're writing something for a marketing-driven section -- you know, with different fonts for headlines and body copy to distinguish it from editorial space -- then, well, you might. Doesn't mean I'd stick one in there unless someone told me to.
Good luck.