I'm looking for Psalms written by David right up until when he killed Goliath. Google so far has been unfruitful.
The answer is no, because there is no real evidence that King David wrote any of the psalms attributed to him. James Luther Mays says in Psalms, page 9, that the personal identities of the authors of the Psalms are unknown. He says the quest for the origin of individual psalms leads to occasions in Israel's public exercise of religion, not to their authors.
Mark S. Smith says in ‘Taking Inspiration: Authorship, Revelation, and the Book of Psalms’, published in Psalms and Practice, page 249 that the psalms “of David” for the most part could not have been written by David since their grammar points to a later period. He says that David ruled towards the end of what scholars consider the period of archaic Hebrew, whereas all the psalms attributed to him (with the possible exceptions of Psalms 18 and 29) are considered to belong to a later stage of Hebrew. He compares the differences as akin to the differences between ‘Beowulf’, ‘The Canterbury Tales’ or Shakespeare, and modern English.
Bruce Feiler says, in Where God Was Born, pages 177-8 that although the Bible attributes many of the Psalms to David, scholars agree that the writing of the Psalms continued for several centuries beyond the Babylonian Exile.
The conclusion, based on thorough studies by biblical scholars and linguists, is that the psalms that eventually came to be attributed to King David were certainly not written by him. Thus, we can not say that he wrote a psalm before the biblical slaying of Goliath.