Wiktionary
vb. (context idiomatic English) to record that someone has offered to help, or contribute something.
Usage examples of "put down for".
Therefore I put down for one of the most effectuall seeds of the Death of any State, that the Conquerors require not only a Submission of mens actions to them for the future, but also an Approbation of all their actions past.
The temporary cots put down for the overnighters were taken up at five and stored away, and the tables unfolded in their place.
By chance I heard from Master Glebus that a horse had been put down for a broken leg.
A certain psalm was recited, and then the letters were noted from which the cock picked up the grains, a fresh grain being put down for each one picked up.
Looks like they figure to put down for the night somewhere around Big Rock Dome.