Set existing picture on my timeline as a my new cover photo W/

This has never been a problem. Setting a picture as a cover photo does not move the picture from when you originally posted (and I say when, because Facebook is time-stamped, which is how you can distinguish one copy of an image from another).

Ok I see but the problem remains: when I click on the picture on my timeline (with the likes and comments) and I click on "Set as cover photo", it just makes a copy of the picture and my cover pic does not come with the likes... Am I doing something wrong? Thanks!

This is not a problem. This is how Facebook works.

Cover photos are a separate copy of an image. You can't transfer the likes over.

Well, so eventually I lose all the likes and comments that people wrote on the pic on my timeline?

No. You keep the old likes, because the image remains on your timeline (unless you delete it from there, which would be foolish).

You have a chance to get a second round of likes.

I feel sorry, English is not my mother tongue, I feel silly... Are we talking about the same thing here? haha

WHAT I would like to do is the following: 2 months ago I posted a picture on my timeline, which got likes and comments. Now, I'd like to set this existing picture as my cover photo BUT I'd like that when people click to see my cover photo, they see the picture with THE SAME amount of likes and the same comments, and not just a copy of the picture, with 0 likes and comments.

I'm not sure if I'm being clear on this...

you are being clear -- but it cannot be done.

the photo is on your wall.
it has comments and likes.

if you make it your cover photo, it will not retain the comments and likes.
but, like jespah said, you will probably get a bunch of new comments and likes...

Oh, you are being perfectly clear.

But you cannot do that.

Facebook makes a copy of any preexisting photo when you shift it over to cover photo status. So you have two copies. One is the original, which has all of the older likes. The second is the cover photo. Never mind that you and I look at them and see them as the same. For Facebook, this is a second 'event' (for lack of a better expression).

But your friends can now like the image a second time, because they will get a notification that the image is now your cover.

Well, that's a shame.

I doubt I'll get a bunch of new likes and comments because since all my friends have already seen the picture, they will just scroll down without noticing it and bother liking it once more...

But anyway thank you for the quick answers!