First album they released it on was in 1980, titled Easter Brothers

From the US copyright office, it looks like they copyrighted every song on the album at once in 1983

Type of Work:        Music
Registration Number / Date:        PA0000160796 / 1983-01-03
Title:        Easter Brothers.
Imprint:        [s.l. : s.n., 19--]
Description:        1 sound cassette.
Notes:        Collection.
Performer:        Performed by The Easter Brothers.
Copyright Claimant:        E B E A Publishing Company
Date of Creation:        1982
Date of Publication:        1982-12-13
Authorship on Application:        words & music: Russell Lee Easter, James Madison Easter & Edd Franklin Easter.
Names:        Easter, Russell Lee, 1930-
Easter, James Madison, 1932-
Easter, Edd Franklin, 1934-
Easter Brothers
EBEA Publishing Company