I had a look on the cateye tripmeter website page and there was nothing under 23 inch directly which got me thinking.... its not a good sign when cateye don't have an entry on its page for cycle computers... so that leaves metric measurements and that initially gave nothing away until I started to think more laterally. 23 inch is 58.4 cm which happens to be 650c...
and low and behold I have 2 entries on the cateye website for cycle computers for 650c that meet your requirements.
So can I suggest you look up 40-584 or 650 x38B as your tyre requirement, whilst not quite 2 inches in width, it is the closest I can find.