David, as part of the nation Israel, will receive forgiveness of sins corporately when Jesus returns for the nation in his 2nd coming. (Acts 3:19-21, 1 Peter 4:17-18, Romans 11),
Romans 11 is the clearest there.
25 For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in.
26 And so all Israel shall be saved: as it is written, There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob:
27 For this is my covenant unto them, when I shall take away their sins.
Note that vs 27 had Paul making the same point in Hebrews 8:8, that the covenant is with Israel, and not us in the Body of Christ
As for Nineveh, if you want to make an argument from silence, that is up to you. Again you should follow your own advice in the last paragraph.