Green’s Dictionary of Slang

agates n.

(US) the testicles .

1941		‘Miscellany’ in AS XVI:3 236: Pig testicles are agates, sheep testicles mountain oysters.
1964		R. Helmer Stag Party 40: Pickle me bloody agates, eh. Never thought I’d see the day.
1973		(con. 1940s–60s) Hogbotel & ffuckes ‘Shearer’s Lament’ in Snatches and Lays 73: I took off his prize ram’s aggots.
1983		R. Aven-Bray Ridgey-Didge Oz Jack Lang 17: Aggots Testicles.
1996		J. Byrell Lairs, Urgers & Coat-Tuggers 308: ‘When they flew the lids he cannoned into half the field like a Walter Lindrum trick shot and then let out a few yelps before squatting down and giving his agates a lick’.
1998		J. & E. Coen Big Lebowski [film script] He says ‘My wife’s a pain in the ass. She’s always busting my friggin’ agates.’.
2001		Darcy ‘Into Temptation’ 🌐 Her hand shot out and grabbed his testicles, squeezing them hard [...] He leaned closer to Elizabeth now and softly kissed her on the cheek. ‘Suppose I say you’re right. Will you let go of my agates, then?’.

In phrases

bet one’s agates (v.)

(Aus.) to make an unarguable bet.

1983		J. Byrell (con. 1959) Up the Cross 33: McGruder mumbled something [...] which you could bet your agates was not at all nice.
1996		J. Byrell Lairs, Urgers & Coat-Tuggers 194: Choko McGruder mumbled something under his breath which you could bet you agates was not at all nice and turned and hurried off .