Green’s Dictionary of Slang

(US) a fig. towel used to mop the tears of self-pitying people.

1928		T.A. Dorgan in Zwilling TAD Lex. (1993) 29: (O [outdoor] S [sports]: Passing by a bunch of big operators who have just joined the I Shoulda Club) That oughta be a good spot to sell cryin’ towels.
1960, 1975		Wentworth & Flexner DAS.