After tales of the sword coast, are you supposed to do black pits next or siege of dragonspear, chronologically speaking? Which is supposed to take place next?

As far as I know, Black pits is just a tiny game, made up by BEAMDOG and it happens during or before even the first game. So I suggest you play it in your own time with different characters since it is not part of the series.

The unorthodox order of the series is:
BG1
Tales of the Sword Coast
Siege od Drangspear
BG2 Shadow of Amn
BG2 Throne of Bhaal.