To laugh on the wrong side of the mouth; to cry. I’ll make him laugh on the wrong (or t’other) side of his mouth.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Lavender * LaunchNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes