I am a member of a social organization called the Hill Country 56'ers.

This organization is extending an invitation to two other groups to join us for a meeting. The invitation reads "Hill Country 56'ers is inviting you ......

I maintain that if you say the club is inviting you this is correct, but if you say Hill Country 56'ers is inviting you this is incorrect and should read Hill Country 56'ers are inviting you .....

Comments?
Ok, toughy; technically nobody would notice if you wrote "Hill Country 56'ers is inviting you.."

But it should be either:

The Hill Country 56'ers club invites you to..

or

The Hill Country 56'ers invite you to..

or even

The Hill Country 56'ers request your company..
www.goodletters.net check here, Im sure it will help you