I am planning an underground feeder to a barn. I am intending to direct bury instead of installing in conduit. I can find various cables (4 wire) that are rated for direct burial, but due to availability right now, I'm not finding the gauges of wires I want. I can find USE-2 wire in the correct sizes. In my reading of NEC, it seems that laying four individual wires in a trench is acceptable, but I can't find examples online of this being done. One other solution I've found is to install a URD 3 wire feeder and add a USE-2 wire in the trench for the 4th wire. Is that acceptable?
USE-2 is sold as cable, not wire, just to be clear on the terminology. It is made of stranded wires wrapped/sheathed in an impermeable cable.
I don't know of any wire types that are permitted under the NEC to bury directly in the ground (though I'm not an electrician, so I haven't ever hunted down every single option). USE and UF cable are the only types of electrical cable that I am aware of which may be directly buried; any others need to be in conduit of some kind.
I would strongly recommend you opt for PVC conduit. It is quite cheap and will allow you to
fix change the wiring you have later on when you discover you want more/different power options out at your barn. Running conduit also means you don't have to dig as deeply into the ground to meet code (it requires 18 inches vs. 24 inches for direct-burial options), and will let you run THHN/THWN/XHHW wires rather than a cable, which are much easier to fish through conduit than cable such as UF or USE, even for fairly straight runs.
What's probably throwing you on USE-2 or URD is that, while they call it "cable", it doesn't have an outer sleeve (compare with, say, XHHW-2 or NM, which does). USE-2 is twisted so it forms a logical cable out of multiple wires. Similar wires by themselves would be sold as THWN-2, which requires conduit.
My suggestion would be to go buy 2-2-2-4 aluminum wire in USE-2 (direct burial). That's commonly used for housing applications and should be easily found (similar copper offerings are exceedingly rare or expensive of late). Otherwise, bury conduit as TylerH suggests.