There are a few glues that are suitable: resorcinal, Titebonds 2&3 and PL Polyurethane Construction Adhesive being ones that I have used successfully. However, these glues need close fits and good clamping pressure, and are not gap filling. The PL advertises that it fills up to 3/8" gaps, but I've read some counter arguments on the WoodenBoat forum.
If your joinery is vaguely sloppy, and/or your frames aren't beveled for your stringers accurately, then you should use a gap filling glue - and thickened epoxy is definitely the best for this, with the PL Premium CA (not their "Gorilla Glue" style glue - this stuff comes in a tube) coming in a distant 2nd. The others should really not be used if your joints aren't good and tight.
A word about the polyurethane glues, such as Gorilla Glue . . . they aren't getting good reviews for marine use, and they, also, require close fits and good clamping - they are definitely not gap filling, even though they foam up and that foam fills gaps (foam is mostly air . . . .).
There are many glue threads on the aforementioned forum, with various anecdotal and scientific observations and opinions.

Pegging and gluing works just fine, though it is only very slightly less tedious than lashing. Screwing and gluing saves a few steps.

Good luck!
Dave Gentry