Jrisebo:
I assume you are actually trying to strengthen and stiffen the floor system, under the tile flooring. Look at the floor sheathing deflection on the existing 16" o/c joists, how much of a contribution is that causing to the overall problem? If that’s significant then you probably want your new sister joist to be fight up under the sheathing to reduce the sheathing span a bit. Alternatively, if the existing joists are the primary problem, and you can get full length 2x8's in there, I’d use them, and have them bearing on the sill plates at each end. You do have to use some engineering judgement and experience about screws vs. nails and their shear values, spacing, etc., but as mentioned above, they do apply some clamping strength while the glue dries. Use a good brand of structural adhesive, not some no-name bargain brand. In either case, an important detail for making this fix work, is that you jack the existing joist up .25 - .5" (to be determined) over the middle third, then fix the new joist to the old, and finally remove the jack. Otherwise, the new joists will not start contributing until some significant added load is applied and all the connections are really brought into play. Obviously, this requires some judgement too, you do not want to be lifting the existing joists off their bearings, or cracking plaster or more tile. But, you do want to partially unload the existing joist and then apply the sister joist, so the new joists are truly sharing the whole load.