Hannon and/or Mahony

Have hit a wall with my great-great grandparents, Timothy Hannon (DOB 1821+/-) and Julia Mahoney/Mahony (DOB 1821+/-). My GEDnumber is NY8912403. Any suggestions, information or assistance would be greatly appreciated. Timothy's US Natualization papers state that he came from Ballinadee, Cork. No information known about Julia's place of birth. 1849 Boston marriage record names Timothy's parents as Daniel and Mary; nothing for Julia. Have found two Daniel and Mary Hannons but neither had a son named Timothy. One couple is from Doneraile and the other is from Killavullen. The only Timothy fitting time/location parameters was born to William HANNAN and Catherine Heffernan in Buttevant. I'm subscribed to GEDmatch but really do not know how to use it. Thanks for accommodating my steep learning curve.