Green’s Dictionary of Slang

(US) to court women, to associate with women.

1887		Lippincott’s Monthly Mag. (Phila.) July 102: For it very frequently happens that the best students do a good deal of ‘calicoing’ [DA].
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.