We are signing an agreement with an organization in the UK who will be marketing a subset of our programs to the UK and Ireland. How do we avoid competing with them online (pay-per-click advertising, etc.) in these countries? And how do we keep them from advertising to people in our region - (the rest of the world)? We currently use pay-per-click ads on search engines such as Google, Overture, etc.

I don't think there is a real definite answer. You can however impose limits on where they can advertise, and what prices they can sell for.

Who is processing the transactions? Amazon.com for example allows affiliates to market their products, and when purchases are made, affiliates get a commission. The same is true for templatemonster.com.

Either way, the sites running the affiliate programs will profit. This might be something you want to look into.

Google AdWords allows geotargeting so that you can avoid advertising in the UK. Part of the contract you sign with them should be that they should take the same precautions to ensure that all of their ad campaigns geotarget only the UK. Aside from AdWords, you can periodically find other advertisers who will geotarget for you. For example, all banner advertising on DaniWeb supports geotargeting.