I have not had success in finding Margaret's last name, but I'm wondering if there would be a town clerk at the most recent city they lived in could be helpful. Also, there are often county genealogical groups that can be a resource for vital records and other relevant information. I hope that a resource in the city of Fairfield or Grundy County might be helpful.
I expect you have seen the 1880 United States Census Info->
Austin GLEASON Self M Male W 67 CT Farmer CT CT Margaret GLEASON Wife M Female W 61 NY Keeping House NY NY Charity T. GLEASON Dau S Female W 21 PA Teacher CT NY
Source Information: Census Place Fairfield, Grundy, Iowa