Green’s Dictionary of Slang

sugar-stick n.

[mid-17C+] the penis.

In phrases

have a bit of sugar-stick (v.) [Puxley, Cockney Rabbit: A Dick ’n’ Arry of Rhyming Slang (1992) suggests rhy. sl. on prick n. (1), but rhy. sl. tends to be coined later]

[19C] of a woman, to have sexual intercourse.

suck the/someone’s sugar-stick (v.) [19C]

1. of a woman, to have sexual intercourse.

2. usu. of a woman, to fellate.