If you go to the signature field's Properties, Signed tab, you'll see an option to execute a script when the field is signed. You can put there something like this (adjust the field name, if required):
this.getField("ApprovedDate").value = "Approved: " + util.printd("mm/dd/yyyy HH:ss", new Date());
(However, I'm not sure this will actually work as you intended when used with multiple signatures in the same file. It's possible it will only work the first time a signature is placed)
.
Visit my custom-made PDF scripts website: http://try67.blogspot.com
Contact me personally: try6767@gmail.com