Infinite Ship Money
Dismantle your entire ship. Talk to dock master. Summon new copy. Rinse and repeat. May only work on sufficiently small craft and only when you first register the ship, make sure you save BEFORE you do this one.
Wisdom Infinite Money
With 20 or more wisdom, Stone Background Blocks sell for $2 to the vendor, but you can buy it back for $1. Rinse and repeat.
Meat Background money
Meat, Blubber, and Shell background get knocked out when damaged, but it's still there in the background (dismantle tool can be used to take it out, or build a ship with this background, you can knock it out with your drill or knife and then have the dock master repair the ship to get it back. Only really worth it with shell, others sell for very little. Takes a long time to harvest shell, so not sure it's a great method.
Stolen Background money
In the starting city there are a couple of fairly high value backgrounds, the white Cloudstone (63 per block) and the red Vulcan Steel (37 per block). If you place anything on the foreground (blocks, machines, workstations, etc), you can get the background to be removable with the dismantle tool. Might also just use these in ship construction!