The telephone line synchronization mechanism is almost certainly a higher voltage / current limited arrangement and would be emulated with a constant current driver mechanism, instead of a low voltage supply where the voltage is set to deliver the rated current based on the coil resistance.
The reason for this is the current rise time. In a simple series resistor inductor arrangement, the time constant t = L/R where L is the inductance and R is the resistance. The time constant determines how fast the current rises in the series circuit when applied from a 0 point. As R increases, t decreases and hence the current builds up faster which is almost certainly a good thing in a mechanical device of this type.
If L = 1H, to put a number to the equation, and R=17 ohms, one time constant = 1/17= 58ms. At one time constant, the current is 63% of the steady state value.
In a typical telephone line system, the DC supply is -48V (in the US, at least. Some EU countries were -54V if I remember correctly.) To limit the current to the rated value, an additional series resistor is used. Plus, of course, the series resistance of the telephone line itself.
Taking our example with 14 ohms coil resistance and 220 mA to take the mid-point of the 170-270 mA values, the total resistance required with -48V DC source is R=48/0.220 = 218 ohms. This resistance would be the sum of the coil resistance, the phone line resistance and a current limiting resistor at the telephone central office.
But look what happens to the time constant; t = 1/218 = 4.5 ms, more about 12 times faster. Hence, the magnetic solenoid pull will happen much faster.
There are other reasons telephone line circuits are configured this way, including limiting short circuit current, and at least in the US, 220 mA would be considered definitely on the high side for maximum sourced current over a normal pair.
All this being said, it is possible to emulate this high voltage driving circuit with a lower voltage and a constant current driver device. The constant current driver can be as simple as a 3-pin fixed voltage regulator -- most data sheets for the 78xx series regulators include a circuit demonstrating how to make a constant current regulator.