Is there an option to print off the Child and Dependent Care Credit form for the individual who took care of our child?

It isn't necessary for you to give the care provider this form.  All they really need to know is the amount they were paid for the child care.  It's best to not give people copies of a form that shows your (and your spouse's, if joint) and your child's full legal name and Social Security number, and also your earned income amount.

Yes, you could try and black out all the important info but you might miss something, not realizing how easily it could  to identity theft.  After all, you don't know who else might see that form.  

For the sake of privacy and protection of your personal information, you could just give them a piece of paper showing the amount you claimed as paid to them.