I searched the IFHF's online database at ROOTSIRELAND.IE. It contains abt 19 million B/M/D records for MOST counties, including Roscommon and Galway. I couldn't find any B records for either Bridget Lyons or Anthony Corey in 1830 +/- 5 yrs.
Your info hints they were likely married in America. Suggest you search the censuses to find their residence on/about/after their likely marriage date. Then contact the RC parishes in that area. Their marriage records, if they survived, might give you more clues.
Note - in 1830s Ireland, not all B/M/D events were recorded, or haven't survived. Suggest you visit this database, register (free), perform your own search, then wait for the IFHF to notify you as more records (if any) are found.