I'm pretty sure you need a 90-91 tranny.

Go to www.car-part.com and search for a tranny for an '89 CRX Si, all you will see is '89 trannies. Then search for a '90 or a '91 tranny. You will see '90 and '91 trannies, no '89 trannies. I take that to mean they aren't interchangeable.

Good luck.