Is one permitted to say krias shema al hamita when they’re drunk?
Yes, if a person is going to sleep when drunk, and this is therefore the only opportunity for this night to say Keriyas Shema al HaMitah, one should say it. This is true for the full Keriyas Shema too (if time is running out).
See Shulchan Aruch, Orach Chaim 99:1; Shulchan Aruch, Orach Chaim, 185 concerning Birkas HaMazon; Mishnah Berurah 185:6; Mishnah Berurah 99:8; 185:6 and Biur Halacha 5 concerning Keriyas Shema.
See also here for more details.