I have a TracFone which would seem to fill that need pretty nicely. You can go to their web page, buy a refurbished phone for $30 and they give you 2 months activation and 110 or 120 minutes with it. At least that was the deal last July when I got mine for a motorcycle trip. The 2 month activation was actually good until November. You can buy cards to add months and minutes at just about any convenience store or WalMart or other store. I later bought a 1 year activation that included 300 or 450 minutes (I forget exactly) which I have not used up yet, and seems like it would fill the needs you state. The cost at this rate is less than $10 per month. It may not be the best deal going, but there is no contract and minutes don't expire as long as the phone stays activated.
web site:
Bill Ranck Blacksburg, Va.