I assume you're using Mac OS X Leopard. First, download and install Lingon. This is a program that makes it easy to manage scheduling for software on your computer.

Now, in Lingon, create a new Launch Daemon, and since it has to be root, make sure it's a Users Daemon. Fill in the following information:

name: com.apple.softwareupdate.scheduled
what: /usr/sbin/softwareupdate -i -a
when: At a specific date (enter your details here)

Save, and then you should be good to go.

(Warning: I haven't tried this myself, but I'm fairly confident it will work. )

Oh, sure ... let's try it on a Guinea Pig first...
OK, I'll bite and give it a try and let you know how it works.
Thank you very much John A.
Jim.

I tried what was suggested but it did not seem to work. Today my Update logo was bouncing up and down on the Dock.
Of course this could indicate two things...
That Lingon did not update my computer or...
The update was new and Lingon never had a chance to do it's thing.
I have to enter my Password when this computer accepts a new download, so how would Lingon do that for me?
I figure that having to update once in a while isn't such a big price to pay, considering how smooth this iMac runs, compared to my old PC or even to my wife's new laptop.
Cheers, Jim.

OK, Thank you, Thank you, Thank you !
This seems to be working very nicely. I haven't had a bouncing update icon on my Dock since the first one that was probably in the que to be installed, since then, so It would appear to working nicely.
So I will mark this as "Solved".
Once again, Thank you ! and Happy New Year ! Jim. ;-)

One thing to keep in mind is that this method doesn't notify you when you should reboot your computer (i.e. after system upgrades). That means that if you never reboot your computer except for updates, you should probably consider rebooting occasionally in case there was an important update that occurred overnight.

Yes ... already thought of that, thanks.
I do a reboot every couple of days just to be sure.
Happy New Year !