Well, the main contenders on the left are all IDE. The laptop drives top right might be IDE or SATA. All my opinion, I haven't tried looking ever for an IDE controller for the A2000 - But - ;-
It's not going to be that easy to get an IDE controller for the A2000. Not without searching a lot of Amiga market places online. Bhudda was one such, there are others listed in the hardware databases, the snag is finding someone willing to sell. Be wary that all will fit, some are Zorro 3 and so only fit an A3000 or A4000.
A good alternative (IF you can find a seller) are the ICD A500 controllers. These work by unplugging the CPU, plugging in the board, and plugging the CPU on top. Very nice solution, but very rare now. They fit A2000s too. Not a card expansion but they do work very nicely.
Now the above 2 paragraphs could be untrue, there might be a commercial source still. I couldn't find one, but like I said, I never really tried to look for one before. Others here are way way more experienced than I am at finding Amiga equipment.