Hello devotchka,
Welcome to the Q&A Board!
I assume you're talking about the date stamped right on the original image and not only when it is printed. Am I correct? There are programs to edit EXIF data and maybe the information can be removed. But digital images also contain imbedded backup data known as Marker notes, so you may have to edit that too.
Let me think about this a bit more.
btw, there must be a camera setting to disable date stamps appearing on your image files.
Related reading:
EXIF http://www.digicamhelp.com/what-is-exif/index.htm