What is the ruling on the prayer of one whose knees pain her when bowing, and is it permissible for her to pray sitting on a chair while being able to prostrate, and does that diminish her reward?

The wording of the question is problematic, and perhaps the questioner means prostration (sujud) not bowing (ruku').

If the questioner is able to perform a light prostration, even if only for the duration of a single tasbeeh (recitation of Subhanallah), then it is obligatory for her. Otherwise, nodding for prostration will suffice, and prostration with the rest of the limbs is waived, because the inability to prostrate with the forehead waives prostration with the rest of the limbs.

She should not prostrate in the manner of bowing. Rather, she should sit and nod for prostration while seated, because sitting for prostration is like standing for bowing. One who is unable to prostrate should nod for it from a sitting position if able. The worshipper must bring her face as close to the ground as possible.

Sitting between the two prostrations is an independent pillar that must be performed when able.