So, I've got a Cobra MR HH425LI VP radio (Marine VHF and GMRS) and am trying to learn if it's possible to make a dual-band J-pole that will serve both bands well. My inspiration are the various Arrow Antenna Open Stub J-Poles. I'm as dumb as a stump when it comes to the science behind antennas, I just know that the 155/460 MHz Arrow Antenna I got works quite well for Marine VHF, but quite poorly for GMRS (which, I understand is no fault of the manufacturer since it wasn't designed for GMRS). Is there some specific harmony between the two bands selected for each antenna, or could I just have one element tuned for 157 MHz and another for 462 MHz?

Very easy to do. Just get some TV twin lead and cut it for the appropriate frequency.

http://www.mtcradio.com/blackbird-vhf-uhf-jpole-base-antenna-mar-gmrs/

This is close.

Gmrs is almost a harmonic of the marine band so a vhf antenna may present a good swr, however radiation patterns might be crazy. Look for the QST article by Ed Fong on his dual band jpole to see what I am talking about.

A 460 antenna should work perfectly for GMRS.