A.T. Robertson Commentary Acts 13:36

"For David, after he had in his own generation served the counsel of God, fell asleep, and was laid unto his fathers, and saw corruption:" — Acts 13:36 (ASV)

His own generation (ιδια γενεα). Either locative case, "in his own generation" or dative object of υπηρετησας (served).

The counsel of God (τη του θεου βουλη). So here, either the dative, the object of υπηρετησας if γενεα is locative, or the instrumental case "by the counsel of God" which again may be construed either with υπηρετησας (having served) or after εκοιμηθη (fell on sleep). Either of the three ways is grammatical and makes good sense. Κοιμαομα for death we have already had (Acts 7:60). So Jesus (John 11:11) and Paul (1 Corinthians 15:6,51).

Was laid (προσετεθη). Was added unto (first aorist passive indicative of προστιθημ). See the verb in 2:47; 5:14. This figure for death probably arose from the custom of burying families together (Genesis 15:15).

Saw corruption (ειδεν διαφθοραν). As Jesus did not (Acts 2:31) as he shows in verse 37.