While I was searching for a date picker to use on a mobile devices, I found one (via stackoverflow: https://stackoverflow.com/a/3023446/2100636) that works with jQuery and ui theming. I am adding this one as an answer because it may be good to consider because it's rooted in the idea of functionality. It has options I didn't see with other pickers, and I think I can incorporate it into a responsive/mobile design pretty well. I'll update with my progress if I end up using it.
From their website, http://www.ama3.com/anytime/, the description below sums it up better than I can. It's also licensed under Creative Commons.
For starters, take a look at these DATE/TIME ALTERNATIVES:
12-hour or 24-hour clock
custom date/time format (countless possibilities, including JSON and XML)
date-only, time-only, or specific fields!
date/time range limits
era-selection (BCE/CE, BC/AD, etc.)
start week on any day (Sunday, Monday, etc.)
custom base for 2-digit years (1900, 2000, etc.)
UTC offsets and time zones
Then peep these STYLING CHOICES:
custom labels/languages
custom CSS styles
jQuery UI Theming
jQuery UI Theme Switcher
jQuery ThemeRoller
pop-up or always-present picker
visible or hidden field
It's also PROGRAMMER-FRIENDLY:
easy to implement
easy AJAX validation
easy Date/String conversion, including JSON and XML
create multiple pickers at once
easy removal
easy to extend
And let's not forget those USABILITY FEATURES:
single-click value selection
double-click select-and-dismiss
WAI-ARIA 1.0 keyboard accessibility
em-based relative-size