Short answer, don't do single axle. Even if you have a 7000lb axle with brakes...if something goes wrong, you're screwed.
Now for the OCD observations:
Some schools of thought say that you only get 74~96 actual cubic feet of wood in a stacked cord, depending on how you stack/cram your wood. In a trailer, you can probably cram tighter because you can wedge things in. If they are smaller splits, and mostly round, I have read that's even more air, and those numbers above are for very little round edged wood (apparently).
http://mb-soft.com/juca/print/firewood.html These numbers are from the U.S. Forest Products Laboratory and other sources, and seem pretty meticulous. Definitely more detailed than other sources, and I tend to trust more detail over less detail.
So on average, you are looking at a 34% loss of capacity on a trailer/truck due to air, if stacked perfectly tight, not going over the sides. I think the only way to do better is to have rectangular splits. You can make up for this by heaping it on top. Good luck with calculating that volume.
So I do this: Calculate your total volume of the trailer capacity, subtract 30%, take that number and multiply it by 50lbs per cubic foot if dry, unless it's green, then you need a better number (I'd say north of 65lbs/cf), and that's what you are likely carrying if it's split normal. If it's round on the edges from smaller logs, you're probably going to have more air. If it's in large rounds, you'll have even more air if you stay below the sides, but more "capacity" because they are easier to stack and tie down, and the rounds have less air, so it might wash out...can't find numbers on that. You will run out of axle quick with rounds, though.
With dual 3500lb axles, you are talking 7k capacity, and most trailers that have enough frame and bed and tires to do one cord are going to weigh 1500~2000lbs (depending on the metal, and the amount of treated wood), so you might get 5000lb capacity out of one, which should get you one cord even if it's hand tossed (if you have the sides, you can do the weight).
And check those tires to make sure they are rated high enough to match the axles. A two cord trailer gets on the super-heavy duty side of things, and you aren't pulling it with a normal vehicle...unless you want a Darwin award.
Anything over 2k lbs should have brakes of some sort. I've yet to see a vehicle rated for over 2k lbs for trailers without brakes. Maybe a dually. Just because people do it, doesn't mean it's smart. I pulled 2500lbs in my trailer, and got stuck in traffic, and had brake fade very quickly, and that was with 4 wheel disk. Add snow, ice, or rain, it gets really interesting. I'm upgrading as soon as I get some money, and I don't tow unless it's sunny outside and never again in traffic.