Brewer's: Cooing and Billing
like Philip and Mary on a shilling. The reference is to coins struck in the year 1555, in which Mary and her consort are placed face to face, and not cheek by jowl, the usual way.
Still amorous, and fond, and billing, Like Philip and Mary on a shilling.
Hudibras, part iii. 1.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894