In reference to the song "The Old Moke Pluckin On The Banjo", my belief is that "Moke" was either a male's personal name or nickname, probably a Black man {given the banjo reference}.

Julia Stewart's book 1,001 African Names {Carol Publishing Group, 1996}, has a listing for this the name "Moke" {moh-KAY}. That editor indicates that in northern Zaire [Congo], "Moke" is frequently attached to male names to mean "junior, little, the younger of the two". For instance, if a man called Molaili had a son named Molaili, the son would be referred to as Molali Moke, meaning "little Molali".
In that sense, "Mookie" could be said to have the same meaning as the "American" nickname "Junior" or "Junie" {a male who has the same names as his father}.

The name "Moke" may have become "Mookie" in keeping with the once ubiquitous American practice of forming male or female nicknames by adding an "ie" or a "y" to personal names {Sally, Susie, Bobbie, Johnny, Ikey, Ronnie, Mandy, Lenny, Debbie, Lindy etc}. I have found a number of Internet references for the name "Mookie" that suggests that this nickname is still given for several male personal names that begin with "M" {such as "Mike" and "Mark"}.

The nickname "Mookie" may be a form of the Hebrew male name "Moishe" or "Moses" which means "savior". "Mookie" may also be a nickname for the Arabic male name "Mustafa" {"Mustapha"} which means 'chosen'. It is also possible that for some people "Mookie" could have been created by rhyming the nicknames "Pookie" and/or "Bookie". Those affectionate nicknames are still given to males and females.

I suppose we'll never really know for sure what was the origin and meaning of the word "Moke" in that old song. But my bet is on one of these names or nicknames.