Green’s Dictionary of Slang

sugar-stick n.

the penis.

[UK]Urquhart (trans.) Gargantua and Pantagruel (1927) I Bk I 152: [note] What our translator calls sometimes the carnal trap-stick (though the ladies call it their sugar-stick).
[UK]Grose Classical Dict. of the Vulgar Tongue (2nd, 3rd edn).
[UK]Lex. Balatronicum.
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue.
[UK]‘Moses Samuels And The Nasty Little Vomans’ in Secret Songster 11: And none but you, my Rachael, shall taste my sugar-stick.
[UK] ‘The Frisky Family’ in Gentleman Steeple-Chaser 36: The father [...] had done the trick, / For hundreds or more, with his long sugar stick.
[UK] ‘The Devil To Pay’ in Rambler’s Flash Songster 41: She went to run away, / But quickly he did stop her. / This is my sugar stick, / So do not cut your luckey.
[UK]E. Sellon Phoebe Kissagen 34: Chloe, do you come also; your little quim shall have my tongue, while charming Phoebe takes the sugar stick.
[UK] ‘Lady Pokingham’ in Pearl 1 July 24: Alice could see the manly shaft as it worked in and out of her sheath, [...] whilst the lips of her cunny seemed to cling to it each time of withdrawal, as if afraid of losing such a delightful sugar stick.
[UK]‘Walter’ My Secret Life (1966) II 314: Remarking that it was a pity such a nice young girl should not taste the sugar-stick.
[Aus]Dead Bird (Sydney) 25 Jan. 2/1: Mamma: ‘Take this pill, Tommy; you’ve been eating sugar-sticks again; your stomach is thoroughly out of order’; Tommy: ‘Go on, ma! as if sugar-sticks ever make boys’ stomachs out of order! It’s only girls’!’ .
[US]B. Rodgers Queens’ Vernacular.
[UK]J. McDonald Dict. of Obscenity etc.

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]

of a woman, to have sexual intercourse.

[UK]Farmer & Henley Sl. and Its Analogues.
suck the/someone’s sugar-stick (v.)

1. of a woman, to have sexual intercourse.

[UK]Farmer & Henley Sl. and Its Analogues.

2. usu. of a woman, to fellate.

[US]Maledicta IV 188: The only way she can supple both ends of it (ie remove its starch) is to suck his sugar-stick.