Are there supplemental rules in AD&D 1e or 2e for playing a PC who's a NPC race — say a kobold or a goblin? The PHB does not speak to this topic, unlike the 3.x SRD.
P.S. I know it's possible to do this by GM fiat, as I RPed with a GMPC goblin in my OD&D party; it's just that it's much easier to work with a GM when you have text you can point the GM at that says "this is allowed, and you do X, Y, and Z to get there." before the GM ever has to make a decision, instead of having to sit down and spend hours with the GM figuring out if it even should be allowed, never mind just how it'd work…
Best Answer
For tools to implement non-standard PC races, you want the AD&D 2nd edition The Complete Book of Humanoids (1993). An excerpt of the back blurb:
Just beware that DMs have the final say. AD&D (whether 1e or 2e) was never balanced with the idea that players could do anything they wanted, so long as it was "rules as written." AD&D is a game that leaves balance in the DM's hands, to customise for their own home campaign's world and their players, so don't try to force any options into the game that your DM doesn't want to offer to the players. (A full-RAW game of AD&D is one that can actually suck pretty hard!)