Constant power load SPICE model
You could use a resistor and define the resistance as a function of the voltage across it. R=V_R^2/power

V_R is the voltage across the resistor (power supply) and for "power" you can use a value for the desired constant power.

I found a link to an example.

edit:

Here is the netlist:

R1 V_R 0 R=limit(0.0001,V(V_R)**2/100,10000)
V1 V_R 0 SINE(11 10 1k)
.tran 0 10ms 0s 100ns
.backanno
.end


for this simulation:

The limits are the min and max value of the resistor and can be changed to any number. But without the limit, the current will rise to very extreme values at nearly or exact 0V across the resistor (R=0). With V_R >> 0V you don't need the limits. In this case the load is 100W. You have to change the number "100" in the formula for R1.