Closest airports to Riverton that I know of where you are likely to find some success:
You can get award tickets to Cody, Wyoming on Delta or United. To Jackson, Wyoming on multiple airlines (only some airlines, such as United and Delta, have year-round service, however). I've usually seen award availability best on United. From time-to-time Delta may open up fairly well award seats to Cody, less often to Jackson (at least during peak travel times).

I don't know if United has any deal with GLA to make award seats available, look on their website or give them a call and ask. But really, flying to Jackson or Cody isn't that bad if you can rent a car and enjoy a beautiful drive over to Riverton.