Green’s Dictionary of Slang

a violent blow; thus tip someone a stoter v., to give someone a blow.

1696		Motteux (trans.) Gargantua and Pantagruel II Bk IV: 327: Vinet lent him such a swinging stoater with the Pitch-fork [...] that down fell Signore on the ground.
c.1698		B.E. Dict. Canting Crew n.p.: Stoter, a great Blow. Stoter him, or tip him a Stoter, settle him, give him a swinging Blow.
1725		New Canting Dict. n.p.: We settled the Cull by a Stoter on his Nob; i.e. We took him such a Blow on the Head as quick stunn’d him.
1737, 1759, 1760, 1776		Bailey Universal Etym. Eng. Dict. [as cit. 1725].
c.1750–1882		B.M. Carew Life and Adventures.
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue n.p.: Stoter. A great blow. Tip him a stoter in the haltering place; give him a blow under the left ear.
1811		Lex. Balatronicum [as cit. 1785].
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.
1834		‘Jack Downing’ Andrew Jackson 26: Every click tell’d; the gineral giv’d Swan sich a stoter on the nob that he reel’d back.
2012		J. Fagan Panopticon 7: He gave me a stoater of a slap yesterday.