What do I need to make a LP-E12 Coupler be powered by either a 18650 or 14500 lition battery?
Given that it uses a 2 series LiIon cells LP-E12 LiIon battery internally the 7.4V input should accept either a  compatible power pack OR 2 x LiIon cells in series.
Either 18650 or 14500 LiIon cells will work.
Keep leads short and use suitably thick wiring.
DO NOT solder to batteries directly.
(Use tabbed cells or spot weld).
4 x AA Alkaline would work - but would almost certainly be substantially less suitable than LiIon cells.  2 x LiIon has a Vminimum of about 6V. 4 x Alkaline at 6V = 1.5V/cell = hardly discharged. Below that the camera may work, or may not.
Typical only ad for LP-E12 here
Canon LP-E12 Lithium-Ion Battery Pack (7.2V, 875mAh)