Wikipedia explains three archaeological studies of the Jericho site, and concludes that the city was abandoned at the time the supposed Biblical battle took place.
How do Christians reconcile the Biblical account with this science?
What is there to 'reconcile'?
If God's word is true (a presuppositional point I take because God cannot lie and scripture comes from God and the 'battle' record itself starts with "The LORD said to Joshua"), then the science will conform to the Bible, and not the other way around.
As to precise dates - we have several plausible timelines. Starting from the creation of the world, I charted [almost] all of the Bible's characters and lives (that we have years on) through Jacob. Based on a whole-years reckoning of lives, Jacob died ~2255AA (After Adam). Based on several other people's work, I agree that the earth was created in about 4004 BC.
That places Jacob's death (in Egypt) at approximately 1749 BC. From a chronological study of Exodus through Joshua I am currently engaged in, but have not published yet, from Moses' birth to the destruction of Jericho is ~121 years (he dies at age 120, and Jericho is conquered within the next several weeks).
That puts the conquest of Jericho approximately between 1534 and 1219 BC - right in the range as shown in the wikipedia article cited for when Jericho was abandoned.
As a sidebar, wouldn't a city appear to be "abandoned" if it had just been completely destroyed?