No More Nails adhesive on PVA primed drywall?
I wouldn't try to primarily use any adhesive for this, it would be better to use a brad nailer. This will be easier, faster and stronger (and cheaper, if you already have or don't count the cost of buying the nailer itself).



Mark the studs, and put a nail in the groove (which will be hidden by the next piece). 

You only really need adhesive for the top row. I'd put it on the bottom row as well, just for good measure, but the bottom row can usually be nailed or even screwed to the wall at the bottom where it will be covered by baseboard.

Since it's not really holding much weight, 'No More Nails' would work, as would basically any silicone or construction adhesive.