I found their marriage listed in a Nicholas County, Kentucky, Vital Statistics Register by John L. Sharp, Copyright 1976, in the Salt Lake City Family History Library. I wasn't looking for it, but was happily surprised. Its part of my attempt to learn more about Nicholas County, Kentucky, the Morgans, the Hamiltons, and why and when they left for Indiana. Family records have them married on January 1, 1833 in Greensburg, Decatur, Indiana. Here is the record I copied.