I have this one for a class machine - It has a decent stitch and a push button but I have never used that feature.
https://www.amazon.com/Brother-Featu.../dp/B000JQM1DE
You could also check Craigslist - as lots of the newer computer machines have push buttons or I did a google search and found this:
http://www.allbrands.com/categories/1940
There are several that are lower in cost and one even for $99.