In these verses the psalmist refers to Yahweh’s promise to David (see 2 Sam 7.12-16). Good News Translation, connecting verse 10 to verses 11-12, has kept in verse 11 the direct form of address, “You,” that is used in verse 10; in Hebrew Yahweh is spoken of in the third person. The sense of verse 11a-b is that Yahweh made a firm promise to David which he will not break.
The language in verse 11c-d is literally “from the fruit of your body I will place on your throne,” which means that one of David’s sons, or a succession of David’s direct male descendants (your sons in verse 12a), will succeed David as king of Israel. The translation should not appear to mean that David would be replaced in his own lifetime by one of his sons; this is why Good News Translation has “he will rule after you.”
The promise is extended to later descendants of David (verse 12); the Davidic dynasty will continue forever to rule the people of Israel. In verse 12 the plural your sons (Revised Standard Version and Good News Translation) may be difficult, for in the nature of the case only one son at a time was to succeed David as king. If necessary, the verse can read “If your son who succeeds you as king is true to my covenant and to the commands I give him, then the succeeding male descendants will succeed you as king for all time.” But it may not be worth the trouble to make it that clear and explicit.
The divine promise will be kept on condition that David’s descendants always keep Yahweh’s covenant with them and obey his commands. Yahweh himself will teach them his testimonies, that is, the rules and laws the people of Israel must follow. For the sake of clarity it may be necessary in some languages to modify the order in verses 11-12 so that “a promise you will not take back” is placed at the end of verse 12. In this way the quoted promise follows directly; that is, “You swore to David when you said ‘I will make one of your sons king … for all times as kings’; this is an oath that you will not break.”
Quoted with permission from Bratcher, Robert G. and Reyburn, William D. A Handbook on the Book of Psalms. (UBS Helps for Translators). New York: UBS, 1991. For this and other handbooks for translators see here .