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Find a pokemon you want to keep, then instead of adding it, make 4-5 runs through the rainbow forest to find berries (among other items) and skip all other pokemon (unless you find one you'd rather have). I found about 7 berries on 4 runs (as well as 2 pass orbs and a heal ball). Doesn't take long at all if you skip all the minigames (and you can go there as much as you want within an hour, so yea).

Also, you should always keep at least one berry spot with oran berries - they only take a day to grow and produce 5 berries for each one you plant.

How do you make multiple runs per visit? o_o