According to online sources like Bulbapedia, it's possible to fish a Feebas on route 2, with a 1% rate.
I tried for a while (at least 250 tries), on both fishing spots around the island in the middle of the lake, and I got nothing. I've caught other 1% pokémon and they were never this long.
I've seen other people struggling as well online, so I'm suspecting you need a condition to make it possible, like an item, a badge or something (I have all badges but haven't done the Battle Tower yet).
Should I just keep trying or do I need to do something in particular?
This question is not "How to get a Feebas?", it's "Is it possible to fish a Feebas on route 2?".