A transformer might be the only acceptable way of getting 120 volts from the two wire 240 volt circuit with ground. The transformer would be expensive if it has to supply more than just a couple of amperes.
If none of the wires is white you may not convert the entire circuit to 120 volts.
ever notice there are only 3 wires strung from a pole mount transformer to a house?
The standard wiring method has a combined neutral-ground (sometimes neutral-ground-guy) wire running between the house and the utility pole. It is supposed to be grounded on both sides, thus the ground rod (or bonding to water pipe) at the house and also there are (should be) ground wires running down each utility pole to ground rods.
Inside the building, once past the main disconnect switch or breaker, ground and neutral must be separate.
There has been talk bantered about (so far going nowhere) about having 4 conductor regular household (single phase) service drops, the ground being separate.