The catalog of the US Copyright Office says:

ALWAYS MARRY AN UGLY GIRL was performed by Humphammer and The Maggie Valley Ramblers on their album "I Like the Bluegrass Sound" (Pigeon Forge, Tenn.: Dash-Dot Productions, 1983)—an 8-track cartridge, apparently.

Furthermore, it says "New Matter [by Rudy Barrett]: words and music of 4 selections; music for 1 selection. ... Preexisting material: 7 selections."

[So apparently we have no way of knowing, from the catalog, whether Barrett wrote this particular song. Maybe the album itself would tell you.]

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WorldCat indicates that ALWAYS MARRY AN UGLY GIRL was performed by The Leatherwoods on their album "Tenth Jam" (Mountain View, AR: Thunder Ridge Castle Duplicating, Inc., [2007?]).