Gary:
The subscription site Roots Ireland does not have a marriage record for John Greer and Bridget Conboy in Co. Sligo. Also, no baptismal records for any children. You didn't mention the religious denomination but many parishes do not have records back to the time before 1842.
The Tithe listings from 1833 show a number of Greers in Kilglass ciivl parish particularly in Leaffony townland. There is a John Greer as well as Michael Greer and William Greer. I don't think the John Greer listed was your ancestor because someone leasing land would likely not be inclined to emigrate. However, your anestor may have been a son of one of the Greers and had no opportunity to obtain land.
Have you considered DNA testing?
Roger McDonnell