to bill and coo

Webster's Dictionary (GCIDE)

Bill \Bill\, v. i. [imp. & p. p. Billed; p. pr. & vb. n. Billing.]

1.To strike; to peck. [Obs.] [1913 Webster]

2.To join bills, as doves; to caress in fondness. "As pigeons bill." --Shak. [1913 Webster]

To bill and coo, to interchange caresses; -- said of doves; also of demonstrative lovers. --Thackeray. [1913 Webster]