The TL072 is spec'ed for a minimum power supply of +-5V. You could try it. The MAX412 is spec'ed for +-2.4V power, but neither is spec'ed for a single supply. It's not hard to create a nice bipolar power supply, so maybe that would be a good idea. Neither chip is rail-to-rail, but if you use a bipolar 15V power supply I don't think that will matter.
If you've got either chip, go ahead and try it.
I did a brief search for the original LMC6582. Now I see why you're looking for alternatives. Not the easiest chip to find, is it? Unfortunately, this circuit pretty much requires an extremely low input bias current. The 66 Mohm resistor only allows a maximum of 75 na @ 5V so the op amp bias current has to be much less than that. Hence, the LMC6582 with its input bias current of 20 pa (max), 80 fa (typical). The article states that the buffer amp needs to have an unusually high input impedance which is what drove the selection of the LMC6582.
Even if you find the LMC6582 or a good replacement, those current levels might require a bit of finesse to get the circuit working properly. But I noticed that Wenzel didn't mention anything about this. I don't understand why. Maybe try normal circuit construction techniques first, but if the results don't seem good enough, you'll have to get drastic. In that case, don't attach either op amp input directly to the circuit board. The leakage through the board could be too high. You'll either need guard traces, teflon standoffs, or just hang the components in mid-air. If you do anything other than guard traces around the input pins, you'll have to bend the input pins so they're not touching the board or socket.
Although the circuit is 'simple', it's not exactly 'easy'.
Ed