Museo (formerly Crane, I think) makes cards specifically designed for inkjet photographic printing:
(That's from the web site of an Aussie supplier, but I'm sure they're well available from US sources.)
I've not used 'em, though, so that's information rather than a recommendation.
I have sent cards out printed on Ilford double-sided matte paper:
either printed as A4 and folded to make an A5 side card or printed on paper cut to A5 size and folded to an A6 sized card. That worked pretty well.