The NFL ring offer was available on boxes of Kellogg's Sugar Corn Pops:
According to the order form, the rings were available for $1.25 plus two proof of purchase seals from boxes of Sugar Pops.
Since the rings were not premiums in the box, but had to be ordered, they are not that easy to come by. I've only seen the Eagles and Steelers rings offered for sale:
The back of the box also mentions an opportunity to join the NFL SuperPro Fan Club, which apparently was advertised on the side of the box.
From this 1985 poster, it looks like the SuperPro Fan Club had a lot of goodies:
By joining the club, you got NFL newsletters, an NFL Standings Board, a team calendar, a decal of your favorite team, a copy of the NFL Fun Book, an official membership card, and an Official Membership Certificate "signed by NFL Commissioner Pete Rozelle"!
From this brochure from 1982, it also looked like there were sweepstakes to win tickets to the Super Bowl:
I'm afraid I don't remember seeing anything about the SuperPro Club when I was a kid. If I had, I surely would have wanted to become a member.