First of all, thanks for your answer!
The method I want to use would be the window.scrollBy(x,y) method, but I'm still having trouble implementing it.
My background script code:
chrome.commands.onCommand.addListener(function ScrollDown(command){ if(command == "scroll") {
window.scrollBy(0,150);
alert("You tried to scroll! :)"); }})
The alert works just fine when pressing the key combination, but it won't scroll down.