How to select the right Operational Amplifier as an impedance converter?
I believe you simply do not have the MAX492 biased correctly. Look at the "Common Mode Input Voltage Range" ("CMIVR") in the MAX492 data sheet. It goes from Vee-0.25 to Vcc+.25. This is the legitimate range of voltage you should be applying to either input on the MAX492.

Since your L-C circuit is grounded to the power supply common, its sinusoidal voltage output will swing above and below ground. On the positive cycle this is OK, but on the negative cycle you are violating the CMIVR of the MAX492 by dipping to far below ground.

You will want to bias the output of the L-C to 1/2 Vcc by make capacitively coupling the L-C output to 2.5 volts and connect this signal to the NI input of the op-amp. This will position the L-C's output squarely in the middle of the legitimate CMIVR. 

You can make the 2.5 volt bias point with a simple resistive divider between 5 VDC and GND. The coupling capacitor needs to have a low reactance at the resonant frequency of the L-C. You have to choose the resistor values (both are equal) so they don't swamp out the L-C's output. I'd start with 20KOhms each and compare results with the unloaded output of the L-C. If the loaded output is significantly swamped, go higher on the resistors.