Peter, I'm pretty sure we are cousins. My great-great grandmother was Mary Ann Trainer, born Simsbury, CT. She is listed with her father and mother James and Ellen Trainer, in the 1850 census in Simsbury. Their son and brother of my great-great grandmother, Peter, was father of William H. Trainer, who was father of William M. Trainer. The twin sons of William M Trainer, William M. Jr and Thomas R., died in Poughkeepsie, NY in 2008 and 2010.
There is a headstone in the Trarriffville Cemetery (Simsbury) that is for Jane Trainer "from Donegall Ireland." I am thinking this might be mother of James as he had a daughter Jane Trainer.
I am looking for anyone who may have information on this family.