Hi Robert,
I have the same issue with time entry. Most web sites are getting the visitors used to using drop downs.
My solution may not work for your situation. However, I find that if you build your own dropdown with a list of times works best, both on a desktop and a mobile device. In our case the times are always in 15 minute increments, therefore a regular NT dropdown is all we need. The Jquery scripts in this URL look nice on a desktop browser. However, you should consider how they will work on a mobile device. I didn't like any of them using a mobile device.
Regards
Bijan