From what Wikipedia says, it looks like you could. The signaling circuitry looks relatively simple; eBay at least has sockets and cables, and a controller board like this one (
http://www.ebay.com/itm/J1772-Active-Vehicle-Control-Board-AVC1-/251068357421?pt=LH_DefaultDomain_0&hash=item3a74d71b2d#ht_500wt_1180). It looks DIY-able with a small microcontroller or even a 555, CMOS logic and a few analog components.
One think I'd probably do, though, is use Level 2 (240V) charging, and run both the chargers off the 240V in parallel (the QuiQs will run at 240V also I believe). The Level 1 (120V) only guarantees 16A, which is right at what two QuiQs will draw, based on what my Kill-a-Watt says. Wikipedia says the 240V is split-phase, but there's no neutral, so I'd be hesitant to run the chargers as "stacked" 120V units like you might in your house.
One other thing Wikipedia is not totally clear on is how you tell the charging station what level to use. There is some signaling to let the EV know how much current the charging station can provide, but I didn't see anything about voltage, unless that's implicit in the current values (i.e., anything <=16A is 120V).
I'm sure some more EV-savvy people on here know more. I only learned how to spell "J1772" about 2 weeks ago
. And there aren't any J1772 stations within 50 miles of me, so the standard US wall outlet is all I have used.