I've been reading Daniel lately, and a couple weeks ago, I found the same sort of translation error that I found in Deuteronomy 9:6 last month. The ESV translates Daniel 9:18 as: "O my God, incline your ear and hear. Open your eyes and see our desolations, and the city that is called by your name. For we do not present our pleas before you because of our righteousness, but because of your great mercy." (The NIV is no better; its translation is "Give ear, O God, and hear; open your eyes and see the desolation of the city that bears your Name. We do not make requests of you because we are righteous, but because of your great mercy.")
As with that verse in Deuteronomy, there's a misplaced "not." It's clear from looking at the Hebrew that "because of our righteousness" is what should be negated, not our "present[ing] our pleas before you." A better translation would be: "We present our pleas before you not because of our righteousness but because of your great mercy."