I second the recommendations above for older Cateye wired. Various members of my family have a MITY 3, a Velo something, and, um, another one. One of them has only one button, that's for the youngest son. I have the MITY 3, and the wife has another one with two buttons that is not a MITY3, but it does have two buttons, and for the life of me I cannot find any difference between them. Every operation is identical, all three of them share the same mount, etc.

BTW, both of my 2-button ones (MITY 3 included) are two-bike capable, which is sweet, because I can mount harnesses on my road and mountain bikes, and just pop the computer back and forth and I have just one odometer to track everything. Just a few button presses to switch between wheel circumferences.