Effective transconductance of a CMOS inverter
Speaking about "transconductance" you are referring to a circuit in which a CMOS inverter is used as a linear amplifier. This is possible if we fix a suitable dc operating point in the middle part of the transfer characteristic Vout=f(Vin). This can be simply done with a feedback resistor RF between output and input. This feedback resistor RF acts as a load - together with an additional load resistor RL (if existent). 

Hence, the effective load resistance is Reff=RF||RL.
In addition, the finite (dynamic) CMOS output resistance r,o is to be considered. 

If there is no signal feedback the input voltage is connected through a coupling capacitor to the common gate terminal and the avalable gain is 

A=gm*(Reff||r,o)

From this we can derive that the effective transconductance is 

gm=A/(Reff||r,o).    

In case the input voltage has an internal source resistor Rin, we have negative signal feedback and the voltage gain is reduced correspondingly.