There is a site out there called TopCoder that offers programming contests at least once a week using C++, Java, VB.net or C#. I imagine if some interprising young programmer were to approach the TopCoder company and explain what FIRST is all about they may host your programming contest for you!
On a side note, if you want some practice with your coding and algorithm skills take a look at
www.topcoder.com and jump in with both feet.
Sean