It's true that a first-party power supply is best, but that's mostly for completeness. It's also true that a cheap or bad power supply is, well, cheap and bad.
That said, every power adapter has a voltage and amperage diagram, which is to say that if you look at the SNES supply, you'll see that it is a class-II power supply with an output of 10V at 850mA, center pin negative. If you find a decent rectifier with (or adjustable to) that output, you can connect it to a compatible plug and it will work just fine.
Assuming 9V is within hardware tolerance, an increase in current to 944mA would result in the same amount of wattage, so that should suffice, and quite probably an increase to a full amp would be 'good enough,' but again going with the proper voltage and at least meeting the current would be best. Given that the OEM supply is a 10V supply, you should really look for 10V at 850+ mA.
I looked a bit, and found these options:
The last one should work just fine, but that's a UK site, so shipping and what-not. The US version (Allied Electronics) does not have one with the proper output current.
Clearly, you're looking at $20+ for the real deal, else scouring local thrift stores for a discarded cord, else rolling the dice on a third-party supply, else building your own.
tl;dr: You want a power supply with 10V output at 850+ mA (a too-high current is not really a problem, but you should try to keep it below 1.5A to avoid wasting a bunch of power). If you find that, get it. In addition, you'll need a compatible plug. That may be tougher, but at the very least a knock-off supply will have this. With these two items in hand, some electrical tape, and a multimeter, you should be able to Frankenstein the power supply together.