Green’s Dictionary of Slang

(Irish) a baby, a small child.

1959		W. Hall Long and the Short and the Tall Act I: Marry them sharpish and leave them with a couple of snappers running round the drum.
1972		B. Hannah Geronimo Rex 263: Those snappers out at the ninth grade that I practice-teach on.
1990		R. Doyle Snapper 66: It’s only a baby, said Bimbo. – A snapper.
2001		G. Coughlan Everyday Eng. and Sl. 🌐 Snapper (n): child.