I couldn't find any specific nightcore browser extensions (which I found rather odd, considering how perfect it would be), so I made one myself. It just raises the pitch and tempo of YouTube videos in real-time. It's called 'Nightcorer' (uncreative I know, but descriptive) and you can find it here (for free) on the Chrome Web Store (if you use Chrome): https://chrome.google.com/webstore/detail/nightcorer/pghhaihcmffdmndjcagdgogjockdnaao
The Web Audio API which I used is still relatively new so they we're a few things I couldn't work around which just makes it so that you have to refresh the tab sometimes to get it to work.
Anyway, hope you like it (and sorry for advertising (I don't like it either (but perhaps some of you could find it useful for at least getting a feel for how a potential nightcore might sound)))