Any of these should work. Scroll down for four channel ones...
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www.newegg.com/Product/P ··· eSize=30As for a built-in 12V supply. Were you planning on sending the 12V over the same coax your video is on? Probably not going to work anyway without some fancy power injector and splitter similar to what power over Ethernet uses.
Speaking of PoE you might want to just rethink your setup and use network cameras and power over Ethernet. You will get a lot longer distance, use cheaper and possibly pre-exixting Ethernet cabling and you won't need a video capture card.