St. Theresa's was erected in 1876, and its earliest parishioners were Irish Catholics who worked on the railroad in Stanley, an active railroad center of that time.
For many years, St. Mary's worked together with St. Theresa's in Stanley. On the occasion of the 100th anniversary of St. Theresa's a combined history was written for both parishes called One Hundred Years in God's Service: The History of St. Theresa's Church at Stanley, New York and St. Mary's Church at Rushville, N.Y. (Note pages 22 & 23 are missing (7.2 MB file)).
Although, there are several saints named Theresa. Our patron is St. Theresa of Avila, founder of the Discalced Carmelites. With St. Catherine of Siena, she was named a Doctor of the Church in 1970, the first two women to be named as such. Her feast day is October 15th. Here are two sites where you can read more about St. Theresa of Avila.