Automatic switch using LDR
All you really need to change is the relay - pick one with an appropriate coil voltage to match your supply.
The resistor values on the opamp inputs all stay the same since they're used in voltage divider networks off the supply - they're 'ratiometric'.
The only resistor you might consider changing is R2 - you could reduce that one a little in proportion to the supply voltage.
So for a 6V supply I'd consider changing R2 to a 5k6 or 4k7.

The LM358 Opamp in this circuit is an example of a "single supply" opamp and its input common-mode voltage range includes ground.
A different Opamp (like the dreaded 741) may not have this feature and so you wouldn't be able to simply reduce the supply voltage and trust in the ratiometric nature of the inputs.