The usual way to derive the input impedance is to calculate the voltage response to a current input. This is simple using Laplace domain impedances with the coil treated as reactance sL and the cap treated as reactance 1/(sC). You have simple linear equations using circuit theory. In other words, Zin=V/I where V is the voltage response to a current I.
It's not clear to me what the "unity buffer" is, unless this is referring to the current source Ix that exactly provides the measured current in the resistance.
Once you find the Zin, the equivalent circuit will be very easy to determine. I'll give you a hint that the final impedance resembles a series RLC circuit.
Active devices are always nonlinear. Hence, you need to make an equivalent AC linear circuit, and then do the analysis on that. Generally, such a solution is valid only for small AC signals at a particular DC operating point (i.e. bias point, or Q-point).
You dont really need an active element to emulate this circuit. The equivalent network is an RLC series circuit with the following values:
Lnew=L
Cnew=C
Rnew=L/(R*C)
So the new network is just a passive RLC circuit with L and C the same as the old circuit, and R is the reciprocal of the original R then multiplied by the ratio of L/C.
If you want to design an active circuit in the same manner of the original circuit you could design a current controlled current source or since R is just a resistance and I=V/R a voltage controlled current source with a settable gain equal to v(R)/R. An op amp could be used if the current is low enough and frequency within range.