not really worth it to keep a Magikarp, since you'll be able to link with Gyarados later on in the game. Though, if you do want to follow standard procedure, you can sit Magikarp in a non-hostile nation, along with some other Warriors you're not using, and set the nation to auto training. it'll take a little longer, but at least you won't have to bring it into battle with you, unlike the main games.
PSN: OniNoMeKyo, Currently Playing: Uncharted 3, Disgaea 4, and Hyperdimension Neptunia Mk 2, until Hyperdimension Neptunia V gets a US release
I just went into the Fire Kingdom's training ground with a Wooper and Magikarp. Not too long after I now have a Quagsire and Gyarados and they come in really handy around the time you need to go to Tererra.
http://oi55.tinypic.com/v5hf8i.jpg I do this music for me. If you was true as me then this for you, but I do it for me.