On Tue, 7 Oct 2014 08:16:11 -0700 (PDT), trader_4
wrote:

2 x 6 for a ceiling isn't unusual, so I'd be surprised if there aren't
recessed lights that will work. You can pull up data sheets online
for the products of interest.

The other issue is loading. If the joists run is in the 6ft direction,
you're good to go. If it's in the 10 ft section, you can probably do
it, don't know what spacing, you'd have to look into code for that. At
10ft, the simpler, better solution might be 2x8. The incremental cost
isn't that much, especially if you have to space 2x6 closer.

I'll toss a wrench in the cog. Would the OP consider use of a track
light unit? I closed a cathedral ceiling space over a living room to
build a floor area ~12 X 21 at the second floor level. Ledger boards
on four sides - Simpson ties for joist, etc. Added electric for
ceiling fan/light below. Granted these were 2 X 10 lumber, T&G 5/8"
(?) ply flooring.