Here are some references from the Roud Index, there are 64 total from all over the UK and North America. I can post some more lyrics later on today or tomorrow . . .

OATS PEAS BEANS AND BARLEY GROWS
Arnold, Folksongs of Alabama (1950) p.135

OATS AND BEANS
Broadwood, English County Songs (1893) p.87 (Lincolnshire, England)

OATS AND BEANS
Gomme & Sharp, Children's Singing Games 1 (1909) pp.16-18 (England)

OATS PEAS BEANS AND BARLEY GROWS
Botkin, American Play-Party Song (1937) pp.254-255 (Oklahoma)

THUS THE FARMER SOWS HIS SEED
Wolford, Play-Party in Indiana (Rev. edn.) pp.211-212

Roud 1380