How does sola fide doctrine reconcile with how much David talks about his own righteousness?

How does sola fide doctrine reconcile with how much David talks about his own righteousness?

Part of the answer lies in the verse you cite;

Proverbs 20:9 Who can say, I have made my heart clean, I am pure from my sin?

There is an agency above whose efforts contribute to righteousness.

The basic problem with the Pharisees was that they thought they had achieved their own righteousness.

While David may not attribute to God on every occasion that his “righteousness” is a result of God working in him, he does make reference to this;

Psalm 51:10-11 Create in me a clean heart, O God; and renew a right spirit within me. Cast me not away from thy presence; and take not thy holy spirit from me.

Faith is what saves. It is counted as righteousness;

Genesis 15:6 And he believed in the LORD; and he counted it to him for righteousness.

We have an example when Samuel sought out David to be anointed King where God revels that it is the condition of the heart (faith/trust) that determines favor.

1 Samuel 16:7 But the LORD said unto Samuel, Look not on his countenance, or on the height of his stature; because I have refused him: for the LORD seeth not as man seeth; for man looketh on the outward appearance, but the LORD looketh on the heart.

So we have righteousness as an effect rather than a cause.

Protestant leaders like Martin Luther, John Calvin, and Charles Spurgeon address these particular verses in their respective commentaries on the Psalms. All three emphasize a difference between David's righteousness before men and his righteousness before God, and that the source of the latter is God's grace alone.

Regarding Psalm 7:8, Calvin answers that David is speaking of a comparison between himself and his enemies, not a comparison between himself and God's standard:

The subject here treated of is not how he could answer if God should demand from him an account of his whole life; but, comparing himself with his enemies, he maintains and not without cause, that, in respect of them, he was righteous. (Commentary on Psalms, v1)

In this he follows Luther, who writes regarding the same verse:

We have before shown [...] that a man's righteousness is that whereby he is unblamable before men and in his own conscience, though that righteousness sufficeth not before God. But the righteousness of God is the grace and mercy of God which justify us even before God. Hence David most carefully adds "my righteousness", that he might distinguish it. (Luther on the Psalms, p 393)

Spurgeon sees David's language in Psalm 18:20 similarly, writing:

Before God the man after God's own heart was a humble sinner, but before his slanderers he could with unblushing face speak of the "cleanness of his hands" and the righteousness of his life. (Treasury of David)

Regarding Psalm 18:20, Calvin notes that it seems that David contradicts himself, as he previously "declared that all the blessings which he possessed were to be traced to the good pleasure of God." Calvin reconciles these statements by saying that God freely showed favor to David, and that subsequently David is blessed by obeying and fulfilling his calling:

Both these things were necessary; first, that God should previously show his favor freely towards David, in choosing him to be king; and next, that David, on the other hand, should, with an obedient spirit, and a pure conscience, receive the kingdom which God thus freely gave him; and farther, that whatever the wicked might attempt, with the view of overthrowing or shaking his faith, he should nevertheless continue to adhere to the direct course of his calling. (Commentary on Psalms, v1)

To those who think that David sounds boastful here, Calvin writes that this is intended for our instruction:

We ought not, however, to think that David, for the sake of obtaining praise among men, has here purposely indulged in the language of vain boasting; we ought rather to view the Holy Spirit as intending by the mouth of David to teach us the profitable doctrine, that the aid of God will never fail us, provided we follow our calling, keep ourselves within the limits which it prescribes, and undertake nothing without the command or warrant of God. (Commentary on Psalms, v1)

Spurgeon similarly remarks that David is right to praise God for rewarding him:

A godly man can see that in divine providence uprightness and truth are in the long run sure to bring their own reward; may he not, when he sees that reward bestowed in his own case, praise the Lord for it? (Treasury of David)

Finally, Calvin makes his belief clear that only God's grace enables us to live rightly, and thus any blessing he gives us as a result of our righteousness finds its ultimate source in his grace:

At the same time, let this truth be deeply fixed in our minds, that we can only begin an upright course of life when God of his good pleasure adopts us into his family, and in effectually calling, anticipates us by his grace, without which neither we nor any creature would give him an opportunity of bestowing this blessing upon us. (Commentary on Psalms, v1)