I have found the Harmon name in Ohio, Oklahoma & Arkansas but not of Irish ancestry. One lady I contacted over 20 years ago assured me that anyone with the surname Harmon from the above areas more than likely arrived in the US in the 17thC. My father's cousin Marianne McDonald married Sam Harmon in Arkansas between 1920 & 1930. On the 1930 census Sam was born in Oklahoma.Marianne's parents came from County Meath & married in Arkansas about 1890, Marianne & her brother John Joseph were born in Arkansas. Maggie Heffernan