Green’s Dictionary of Slang

(US) to court women, to associate with women, thus n. calicoing, courting, calicoist, a womanizer.

1886		Conservative (Carrolton, MS) 27 Feb. 5/3: Wanted to Know [...] Why John didn’t go calicoing Friday night.
1887		Dly Sentinel (Rome, NY) 26 July 4/4: [A] ‘calicoist’ (which implies a greater lover of the fair sex than of his studies).
1902		Richmond Dispatch (VA) 13 Apr. 9/2: The fair ones of Ashland [...] were in abundance, and the ‘non-calicoists’s’ heart sickened as he looked upon the striking spectacle of beautiful ladies.
1905		J.W. Carr ‘Words from Northwest Arkansas’ in DN III:i 73: calico, v. To call on a young lady. ‘I’m going calicoing’.
1915		L.R. Dingus ‘A Word-List From Virginia’ in DN IV:iii 181: calico, v. To pass one’s time with ladies.
1921		Roanoke Times (VA) 23 Jan. 2/7: [of student play performances] John Roemer, as the calicoist, Jim Hennelly, as the goat rusher [...] were good.