Q. Hey-lo Oracle person,
If I cover a Coldplay song and it is slightly successful, would I have to pay royalties on said song? How would I go about that? Or does Coldplay not even care?

Gosh, I admire your self-belief and confidence and maybe it's a good thing to consider such things but you may be a little ahead of yourself here Ben.
Anyone can do a straight cover of another's song; it's when you sample sections of a song it becomes a more complicated legal issue.
There are mechanical licenses available for such purposes too but I would strongly suggest you get legal representation (assuming you haven't got a manager/label etc.) if you intend to release a cover.
The fact that you did not write the song means that you would not get any money from the publishing income generated. Coldplay are signed to a publishing company who would collect those royalties.
There is a long process to go through before then though. For instance you'd have to record it, get some kind of release, receive some kind of promotion/radio play and then sell it and hope people buy it...