Excluding the starters, as they can all be shiny from gens 2-5. Here's a list of all gift Pokemon from Gens 2-5 that can't be shiny.
Kenya the Spearow (Predetermined)
Shuckie the Shuckle (Predetermined)
Both Zorua (Predetermined, Shiny locked)
Sources: Every single Serebii Page for each game's gift Pokemon. Also a bit of experience