Hi Kyle,I am Pete, and I'll be happy to assist with your photo question.
There are no photo printing services that I am aware of that will add the date for you.
However, you can do this yourself quite easily to a batch of photos before sending them for printing. You can make a copy of the photos and save them in a separate folder before adding the date, so that you still have the originals in case you need them.
There are many some programs that will allow you to add the date taken to a batch of photos automatically.
The best program is probably Date Me Now: http://www.ketara.ca/print-dates-on-photos.html
If you have Photoshop Elements, or another advanced photo editing program, it may also have an automatic date stamp capability.