There are a couple of ways to do it, but you are going to have to code some custom script, regardless of how you end up doing it.
1 - Create a small script on your own store space which just displays a random banner, and then embed this page within an iFrame on your other site. Messy, but secure, as no passwords or database access is needed by 2nd site.
2 - Create a little javascript file on your own server which builds the banners for you. You can then include the javascript as a linked file within as many sites as you need, muchthe same as Google does with their advertising.
3 - the worst way to do it, but it may work depending on your server setup and permissions - use the
Sidebox Anywhere contrib to place the sidebox within your other site. You will need to have the correct permissions as you will need to be able to include the store files within yuor other PHP script.
If it was me, I would go for option 2 - it's a little more work, but it is far more flexible, and can be re-used at a later date with loads of sites, rather than just one.
Absolute