2D Tracking of an object - which sensor?
I feel that an array of IR transmitters and receivers could work for you.

If you put the transmitters/receivers in an recessed tube with (black, non-ir reflectant) separations, you can avoid crosstalk.
You should be wary that it may require some tweaking to find the right sensitivity.



Here is a video (and here) that shows this in practice. I like the fact that you don't need sensors on either side of the object.

You may also consider video-processing, but that's out of scope for Arduino.
Or use a Lidar.