Records for marriages, as well as others, for the early years of Shelby County, including 1870's are located at the Shelby County Historical Society, 1854 Old Courthouse, P.O. Box 457, Columbiana, Alabama 35051-0457.205 669-3919.
Transcripts and index's of many old records can be found on the Historical Society Web Site. I don't think that 1870 marriages are posted though. Hope this helps