Table: Armor Class Modifiers has an entry for kneeling or sitting, but Pathfinder's rules explain nothing else about kneeling or sitting except that a melee attack launched at a kneeling or sitting creature gains a +2 bonus on the attack roll and a ranged attack launched at a kneeling or sitting creature suffers a −2 penalty on the attack roll. Strictly, then, the GM adjudicates any other mechanical effects incurred from kneeling or sitting, like what action is required to kneel or sit, or if standing up from kneeling or sitting provokes an attack of opportunity from each foe that threatens the kneeler or sitter.
By the way, that entry on the Pathfinder chart Table: Armor Class Modifiers is mirrored on this chart of the same name in the System Reference Document, the stripped down version of Dungeons & Dragons 3.5 that Pathfinder used as the starting point for most of its rules. (Also see Table 8–6: Armor Class Modifiers (Player's Handbook (2003) 151).) In that earlier game, kneeling and sitting are also equally undefined and puzzling.
In fact, that entry dates back to Dungeons & Dragons, Third Edition, before the 3.5 revision, as can be seen in this earlier SRD in the section Attack Roll Modifiers on the chart Table: Attack Roll Modifiers. (Also see Table 8—8: Attack Roll Modifiers (Player's Handbook (2000) 132).) It's meaning is opaque there, too.
However, Skip Williams's Rules of the Game column "All about Movement (Part Two)" (June 2004) for Dungeons & Dragons 3.5 includes the following as part of its Stand Up from Prone entry:
Getting to your feet when seated on the ground is just as difficult as getting up from a prone position and also requires a move action that provokes attacks of opportunity. If you're kneeling on the ground, getting up takes some time, but it doesn't make you vulnerable, so you use a move action that doesn't provoke attacks of opportunity. Getting up from a chair is a free action that doesn't provoke attacks of opportunity if the chair is fairly high; otherwise it's just like getting up from a prone position.
(Along with Monte Cook and Jonathan Tweet, Williams is one of the original big three designers of Dungeons & Dragons, Third Edition; specifically, he's credited with writing that edition's Monster Manual.) Williams's columns sometimes take heat from readers because the columns go beyond their mandate of just explaining the rules that are present and offering what appear to be modified rules or brand new new rules that go well beyond the text. (Also see this question.) The rulings in Standing Up from Prone are no exception. Even though Williams makes what seems to be perfectly reasonable suggestions for adjudicating kneeling and sitting, no other text actually includes these rules. How Williams developed these rules likewise remains unstated. (Were these rules the product of rigorous playtesting and simply accidentally omitted from the printed rules? Or were they just fabricated for this article and eyeballed for their utility?) Nonetheless, this may be as close to official word as we're going to get.
As an aside, I suspect the paragraph describing all this kneeling and sitting jazz ended up on the cutting-room floor to make room for what the designers envisioned was more important stuff. Seriously, combat in Third Edition—therefore in Pathfinder—is a lot like combat using the Player's Option: Combat & Tactics (1995) for Advanced Dungeons & Dragons, 2nd Edition, and that book has an entry on Sitting, Kneeling, and Lying Prone. In part, it says, "Characters may sit, kneel, or fall prone as a no-move action. Getting up from sitting or kneeling is considered a half-move action, so a character can stand and still fire a missile or make an attack" (30—1). When the basis for the game's combat system has a section that clear, it's not like the designers could be unaware that folks could engage in battle while sitting or kneeling.