Lets call it "Adcoin" or "AffiliateCoin" and you can only mine it by watching ads or videos etc.
I envisage it as being like the coins that you mine using BOINC where you have an ad program that runs and you can only mine the coins if it is running at the same time, possibly needing to solve captcha's as well.
The cryptocurrency mining works in some other way but seeing your idea we can have two ideas either you have to make a coin which will be mined 100% and you will give it to those who will complete a task or you can create a system in which you will show some ads on the screen of mining desktop.