I wonder if there's actual written-down lyrics to Bill's vocals in the title song (composed by the great Quincy Jones IIRC). Best as I can recall them after about 35 years:
HOOO law! Gonna get some...RAGGITS and some ROLLS and REEZamyalin ha ha ha! Everyday Long as I'm away
Cos was doing these nonsense words during his early stand up bits. If you listen to "A Nut In Every Car" off of his first album, you'll hear those same type of nonsense words that he later used in "Hicky Burr". The Monkees were just using stuff they heard on his early comedy albums, and not directly borrowing from the theme to "The Bill Cosby Show"
The nonesensical food references Cos sings in the theme song are his recollections of his grandfather's speech patterns when Bill was just a adolescent. You can get the full length opening and closing theme in a seamless song on the Bill Cosby-Quincy Jones Cd titled Original 1969 Jam Session which also has an extended version of the the theme song as well as some of the background music heard throughout the series This Cd was released about 2-3 years ago and has some outstanding jazz men playing with the Quincy Jones band, a very funky and swinging recording session
A five-minute version of the song can be found on Quincy Jones' 1971 album Smackwater Jack. Also, the CD The New Mixes Vol. 1 contains remixes of much of the material on The Original Jam Sessions, and some of the remixes feature samples of Cosby's vocal interjections from 'Hikky-Burr'.