Green’s Dictionary of Slang

boners v.

also bonas, boney, bonny, boney-eye
[? pidgin bon eye, good eye]

(US juv.) to claim possession of something; also as excl., that’s mine!

[US]DN I 384: Bonas [...] in phrase ‘I bonas it’ = ‘I claim it’ or ‘I take possession of it.’.
WELS Supplement n.p.: I bonny that one — for dibs or druthers: ‘I bonny that piece of candy.’ ‘I bonny that dress when you outgrow it.’ Used by children at school, especially by girls.
[US]in DARE I 329/2: (When one persons wants to share or divide something with another person...) Divvey; halvers; boners.
[US]in DARE I 330/1: [...] (as of c 1925), I boney-eye [...] the red one. When you want something among a choice of articles. For instance, several children ... looking at several trucks. If a child likes the red truck he might say ‘I boney-eye the red one.’ Then none of the other children can choose the red truck.