The earliest Christian picture is almost certainly the mosaic on the floor of a church in Madaba, Jordan from the 6th century CE(predating Islam altogether!) The map is of most Biblical places and the Jerusalem part is fascinating:
Many other ancient maps of Jerusalem, from the 12th through 19th centuries CE, can be found here.
Perhaps pre-dating this one is a map known as the Peutinger Map, drawn in the 12th or 13th century CE that was apparently an exact copy of a 4th century Roman road map that included Jerusalem. This is far more a map than a picture, though:
An Islamic map of the area from the 10th century is fascinating for how it represents Jerusalem (one of the upper circles):
The Arabs never regarded the Land of Israel, which they called Falastin, as a distinct geographical or political unit, and mapped it as an integral part of ash-Sham, Syria, as in the example shown here. Jerusalem is represented by one of the circles in the upper part of the map (which is directed towards the south-west and is named Bayt al-Maqdas (Hebrew: Bet haMiqdash, the Temple).
I imagine the earliest picture of Jerusalem in Jewish art would probably be in one of the famous illuminated Haggadahs from the 15th century CE on the page where it says "Next Year in Jerusalem," but the earliest I could find was this one from a this early printed Amsterdam Haggadah (1695):
One of the first photographs of Jerusalem was taken in 1844 by Jiro De Franje:
This picture is a mirror image of the way Jerusalem looks.
I cannot find any Muslim artwork of Jerusalem specifically before the 20th century. Again, if someone can point me to an earlier picture I will post it.