Green’s Dictionary of Slang

1. (US black) to relax.

1936

D. Burley in Chicago Defender 16 May 19: Back Door’s Revised Dictionary [...] gettin’ my kicks — Padding down with ‘tea’.

2. (US black) in fig. use, to accept, to accustom oneself to.

1954

W.G. Smith South Street 99: ‘But you’re ofay, cherie; tough, I know, but you might’s well pad down with it. The jive put down by Claude and me is strictly boot stuff, got to be. You can’t dig it; I can’t school you.

3. (US black) to live somewhere; to accompany someone.

1961		R.A. Norton Through Beatnik Eyeballs 40: He done had one witch who pad down with him some months.
1969		‘Iceberg Slim’ Pimp 111: I had told her to work just the block where we padded.
2005		B. Hare Urban Grimshaw 310: Skeeter and Frank were recently padded up together in the same jail.
2011		J.J. Connolly Viva La Madness 25: Me and Sonny in the rental, Roy and Morty padded up together.