I found several old versions of this song classified as "college songs." Apparently none of these versions are cumulative, unless the editors simply omitted to notate this feature.

From Songs of Yale: A New Collection of College Songs by Charles S. Elliot (New Haven, Conn.: Charles C. Chatfield & Co., 1870):

(That book also has musical notation.)

OH, THAT WILL BE JOYFUL

1. The man who has plenty of good peanuts and giveth his neighbor none,
He shan't have any of my peanuts when his peanuts are gone.
When his peanuts are gone, when his peanuts are gone,
He shan't have any of my peanuts when his peanuts are gone.
Oh, that will be joyful, joyful, joyful,
Oh, that will be joyful, when his peanuts are gone.

2. The man who has plenty of good soft, sweet soda crackers and giveth his neighbor none,
He shan't have any of my good soft, sweet, &c.
[No further lyrics are given.]

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From Carmina Collegensia by Henry Randall Waite, 1876:

THE MAN WHO HAS PLENTY OF GOOD PEANUTS

1. The man who has plenty of good peanuts and giveth his neighbor none,
He shan't have any of my peanuts when his peanuts are gone.
When his peanuts are gone, when his peanuts are gone,
He shan't have any of my peanuts when his peanuts are gone.

2. ...plenty of good oranges...
3. ...plenty of soft, sweet soda crackers...
4. ...plenty ripe, red strawberry short cake...
5. ...any salt-junk...
6. ...spondulacs...

[WTF are salt-junk and spondulacs?]

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From College Songs and Popular Ballads for Guitar by Emma Schubert, C W Bemis, W W Harris, H. W. Harris, 1888:

PEANUT SONG
Arr. By G. W. Bemis

[Same lyrics as in Carmina Collegensia, also with musical notation.]

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From Carmina Princetonia, 1890:

PEANUTS

1. [Same as from Songs of Yale, above.]
2. ...good soft and sweet soda crackers....
3. ...good lonejack smoking tobacco....
4. ...stale old roasted chestnuts....
5. ...Lorillard's fresh fine cut unadulterated chewing tobacco....
6. ...de-monetized, de-moralized, de-generate, unconstitutional, saponaceous silver money....
7. ...Richmond straight cut cigarettes of delicate flavor and highest cost tobacco....
8. ...chestnuts....

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There are more versions out there if you want to collect them. I selected the oldest I could find, omitting brief quotes. I suggest you search for "and giveth his neighbor none" (in quotes).