If your reason for not using cron is that it is not available on the box, then you could consider using cron on a separate box and having it call a cgi script on your server at the given times (obviously with some authentication). Of course you need a separate box for this to work.
Also, you could do a google search on 'cron service'. I noticed a few companies that offer cron like services (although I have never used them, and could not give you a recommendation on them)...
Update: Now that I know your reason for not wanting to use cron, I realize that my answer doesn't help you one bit. So you can ignore this message. For future questions, the more info the better. There is no such thing as too much info (There is always the 'readmore' tag if you are worried about the length of your post). Sorry I couldn't be of more help, but it looks like you got some good answers below...
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