Sea pickles have interesting properties, which can be exploited to farm them. One pickle can be placed on live coral and then have bonemeal applied. After one bonemeal is applied, three more sea pickles will be placed in the same block. The application of more bonemeal causes them to spread to nearby live coral blocks.
Manually farming sea pickles can be done underwater near a coral reef. Simply apply bonemeal on as many live coral blocks and sea pickle blocks as possible, and the player will soon have a lot of sea pickles.
To make the farming process easier, a dispenser can be hooked up to a fast redstone clock. This dispenser will apply bonemeal to a water source block on top of a coral block. The coral is kept alive by the water above it. The player then plants and breaks the sea pickle accordingly.
Farming sea pickles while away from keyboard takes a bit of redstone. First, the player must plant a sea pickle underwater on top of a coral block. A dispenser puts bonemeal on the sea pickle, causing it to multiply to 4 pickles. Then, the block underneath the pickles can be moved, or they are directly broken with a piston. The challenge is that a block update detector cannot be used for this since water spontaneously causes block updates.
This takes advantage of the spreading mechanic of sea pickles. To build automatic sea pickle farms, have a dispenser apply bonemeal to a block of 4 sea pickles, with another coral block nearby. The sea pickles will spread to this other coral block, which can be detected and broken.