How can I attach a 2x to a deck joist to give more room for stair stringer?
I attach the 2x6 right to the face of the 2x10 joist. With an 8" rise you will have 2.5" to attach it too.  I use alot of nails and a few ledgerlock lags. I also always double the outside joist. I never had an inspector question it. If the bottom your steps are firmly attached by burying posts the stairs can not fall down.