They cant be a large group of (sick) people doing this, probably it's one person. So I suggest tracking his posts, capture his IP and ban the IP range for an effective solution. Also enabling moderation for new users can help. So does approving new members while they register (together with "who might this new user be?" hack).
But here is the hack anyway. And IMO it's a little bit better than you asked because it does not reject the posts but just put them into moderation so you wont lose legitimate posts either.

You can approve/reject posts in the morning..
Edit newthread.php, find:
PHP Code:
$visible=iif($foruminfo[moderatenew],0,1);
After that insert:
PHP Code:
// Moderate Users Hack
if ($bbuserinfo[usergroupid]==X AND (int)date("H", time())>0 AND (int)date("H", time())<9)
{
$visible=0;
}
// Moderate Users Hack
Replace X with usergroupid. You can also edit 0 and 9 according to your wishes. With these numbers usergroup X's posts between 00.00 to 09.00 AM will be moderated in your board in all forums.
Insert the same code to newreply.php after line:
PHP Code:
$visible=!$foruminfo[moderatenew];
I didnt test it but it should work, if not holler and I'll fix it..
By the way, time is calculated according to your server time so set banned hours accordingly.
Enjoy!

Logician
Ps. he can still send pms though, so you better get him and ban his IP.