The gemora in Baba Basra lists 10 people that co-authored Tehillim with David

דוד כתב ספר תהלים ע"י עשרה זקנים ע"י אדם הראשון על ידי מלכי צדק ועל ידי אברהם וע"י משה ועל ידי הימן וע"י ידותון ועל ידי אסף ועל ידי שלשה בני קרח

Yet in psalm 132 it seems the psalmist is Solomon, talking about an event that occurred after David had passed:

תהילים קל״ב:י׳
בַּֽ֭עֲבוּר דָּוִ֣ד עַבְדֶּ֑ךָ אַל־תָּ֝שֵׁ֗ב פְּנֵ֣י מְשִׁיחֶֽךָ

Which Rashi explains is Solomon praying that in the merit of his father David, the Solomon Temple should not be rejected:

אל תשב פני משיחך. שלמה בבואו להכניס שם את הארון:

Inevitably someone will say that David wrote this prophetically, but that seems like quite a stretch given he would be talking about himself in the third person.