It's not on top of Mt. Coronet. It's in Mt. Coronet.
In order to find Feebas in Pokemon Diamond or Pokemon Pearl or Pokemon Platinum, there are a few things that you must have before you can go out and try to capture them:
1. A Pokemon that knows the HM 03 Surf :)
2. A Pokemon that knows the HM 06 Defog :)
3. A Pokemon that knows the HM 04 Strength :)
4. An Old Rod.
After you have all four of those things, Fly to Celestic Town and go west onto the Route there and enter Mt. Coronet through that entrance. After you enter Mt. Coronet there, you must head north and push aside the boulder that is blocking your path with Strength.
After that, head north and then west when the tunnel heads west (left). Go down the stairs and you should be in an area with a lot of fog. Use Defog and head west and then north, making sure to make your way down to the huge lake in this area of Mt. Coronet.
After you get to the edge of the water, use Surf and Surf all the way into the upper-right hand corner. From there, move 1 tile left and turn around and fish in the upper right hand corner. Make sure that you have the Good Rod set to the Y Button so that you can easily access it. Fish twice in the upper right hand corner, then move back into the upper right hand corner and turn left and fish twice in the tile directly left of you.
Continue this pattern until you finish that row, then fish twice in the tile directly down from the end of the row that you were on and then head back towards the upper-right hand corner (the row below it), fishing twice in every tile there is in that row.
Continue this process throughout the entire lake or until you find a Feebas.
Feebas only appear in 4 of the massive amount of tiles that are in the lake, and they only have about a 10-25% chance of appearing, so you might have to fish in every tile more than twice :)
Oh, I forgot to mention that the tiles that the Feebas appear in are completely different in every single game. While your friend might have found a Feebas in the upper-right hand corner tile, you might not.
BTW, worry about the bold part.