Custom Tab-Shaped Plug
The simplest option I can think of is a simple pcb edge connector.  The device would have the edge of a PCB sticking out, with suitable copper pads on it.

The clip would use an off-the-shelf card edge connector to make contact with the PCB.

If polarity isn't a problem, just a big copper pad on each side of the PCB would do.  Otherwise a cunning arrangement of copper "fingers", lining up with the contacts in the edge connector, such that the polarity remains correct even if the device is plugged in the opposite way wound.