Green’s Dictionary of Slang

granny n.2

also grannie
[ety. unknown]

(US) a dollar.

[US]A.J.H. Duganne Camps and Prisons 421: ‘Fifteen dollar fur dis yer, an’ ten dollar fur dat dar’ [...] ‘Dry up, old cotton-head!’ ‘Fifteen grannies!’ ‘What’s Confed. money worth?’.