There are special effects (psionics, magic, etc) which can cause blindness or deafness, but are there rules for being blind or deaf from character birth or becoming so from injury?
I am not aware of any
...and I am reasonably confident that my knowledge here is fairly comprehensive.
There definitely isn’t anything in Player’s Handbook, Dungeon Master’s Guide, Player’s Handbook II, or Dungeon Master’s Guide II. There isn’t anything in Unearthed Arcana. Rules Compendium doesn’t mention it. And every other supplement is tailored to some particular facet of the game (certain classes, certain races, certain monsters, certain environments, etc.), rather than “global” rules like this would be, so it’s very unlikely to be in any of those.
That pretty much just leaves Dragon and Dungeon magazines. I do not have comprehensive knowledge of what’s in those, per se, so it’s plausible that it can be found therein. If anything is found, however, it is assured to be awful—Paizo’s game design is rarely strong, and this particular problem is, I’m fairly sure, literally impossible to balance. Blindness, in particular, is so monumentally debilitating that being an adventurer while suffering from it is basically implausible. To become an adventurer, magic would be necessary to cure or circumvent the blindness, and likewise, if an adventurer becomes blinded (and it doesn’t clear up on its own), curing or mitigating that has to be the first order of business. Even the blindfold of true darkness (Arms & Equipment Guide) is an item of questionable utility, and that gives blind-sight out to 60 feet, which is amazing. Anything less than that—and barring magic, we should expect less than that—is going to create a character who is unable to convincingly adventure with the rest of the party.
There is a Variant Rule on page 27 of the DMG called Damage to Specific Areas.
Sometimes, despite the abstract nature of combat, you’re going to want to apply damage to specific parts of the body, such as when a character’s hands are thrust into flames, when he steps on caltrops, or when he peeks through a hole in the wall and someone shoots an arrow into the hole from the other side. (...)
The rule suggests to apply a –2 penalty to any action that the character undertakes using that portion of his body. There is a table that shows which actions would suffer this penalty. It also says that
Severe damage to both eyes causes a character to become blinded.
Severe damage to both ears causes a character to become deafened.
Do rules about not becoming blind count? The Shadowspy from Complete Champion has this odd benefit:
Immunity to Blindness (Su): Beginning at 2nd level, you cannot be blinded by magical effects, spells, or bright light. Physical barriers to sight, such as blindfolds and solid objects, still prevent you from seeing. Additionally, any wounds that cause the destruction of your eyes still blind you.
I don't know why they put it there, but it appears that the authors of Complete Champion thought that wounds that cause blindness were a thing in the system. It might be worth skimming that book for any features that may cause it.