Would anyone know how to locate birth or baptism records for Ulster County for 1827-1830 other than guessing at a church affiliation and looking for records that way?

Specifically, I'm trying to find the birth of a Sidney W. Wood who was b. abt. 1829 in Kingston, Ulster County, NY and the child of Isreal Wood and Julia Watkins. I have tons of information on this family after they moved to Galen, Wayne County, NY in the 1830's but would like to find Sidney's actual birth or baptism record.

Thanks for your help, Petey