Well, a UNIX timestamp, or a MySQL one? Hmm, 8 characters....
I'm not up on the mysql "Date" stuff too well. IIRC, there's a CURRDATE or CURR_DATE or somesuch. If you want a UNIX timestamp:
$connect= mysql_connect("localhost","root","cpyter")
or die("Could not connect to database in localhost !");
$result=mysql_select_db("testdiw")
or die("Could not select that database !");
$now=time();
$sqlquery = "INSERT INTO deponent VALUES('','$now','". $deponentname ."','". $casenum ."','". $forumst ."','". $county ."','". $plaintiff ."','". $defendant ."')";
$queryresult = mysql_query($sqlquery) or die(" Could not execute mysql query !");
Of course, if your field type is a MySQL Date field, it won't work. Would have to be bigint, I'd think.