Six Tiles
Each space that your character occupies is considered a tile. A Feeba can inhabit only six different tiles of water in Route 119. It has a very high encounter rate on the tiles it does inhabit, so if you don't encounter it in a couple of tries, switch spaces. Route 119 is rather large, so keep track of the spaces you have and haven't tried by moving in a specific pattern.
Super Rod
Any fishing rod will work to capture Feebas, but the Super Rod gives an advantage. The Super Rod is the highest-quality fishing rod available. It can be obtained by talking to a fisherman in Mossdeep City. Higher-quality fishing rods will only make high-level Pokemon appear. With the Super Rod, only Carvanha and Feebas will appear, which means you don't have to sort through a lot of unwanted Pokemon.
Dewford's Trendy Phrase
Dewford City is a small island located in the far south east of the Hoenn region. Talk to a boy outside Dewford Hall to change the "Trendy Phrase." The phrase, which can be any assortment of words, affects the things the townspeople say. It also refreshes the six tiles in which Feebas spawn on Route 119. If you're stuck, this can help.
Trade
If you're having terrible luck catching Feebas, there is an option to trade Pokemon. Connect over Wi-Fi and trade Pokemon with a friend who has Feebas. Pokemon Emerald has only limited wireless capability, so you will have to be right next to your friend and have plugged in the wireless adapter that came with the game. Go to a Pokemon Center, which can be found in any town, to connect between games.