A resistor can be used but it isn't pretty.
If you know the coil voltage and and the coil resistance then you can determine how much current travels through the coil and how much power it is dissipating while energized.

Using round values for an example: 48V source and a 4 ohm coil -- you have (48V / 4 ohms) or 12 amps.
During the on period - the coil is dissipating (48V * 12A) = 576 watts. That puppy is going to get hot if locked on!

Adding a series resistor will lower the voltage drop across the coil which will reduce the current flow and the power dissipated (and physical power transferred to chime).

Suppose you add a 1 ohm (pretty high value) resistor in series with coil:
(48 volts / (4 ohms + 1 ohm)) = 9.6 amps. You have reduced the coil current and power to 80%.
Power dissipated by both coil and resistor = (48V * 9.6A) = 460 watts. A lot less but still quite a bit.
Power dissipated by coil only = ((9.6A * 9.6A) * 4 ohms) = 368 watts.
Power dissipated by resistor only = (9.6A * 9.6A) * 1 ohm) = 92 watts.
In a locked on coil - it will be a race to see which burns up first - the coil or the resistor (assuming the fuse doesn't blow first).
Theoretically, for the resistor to survive and everything else still burn up - you need a 200W resistor (don't go above 50% rated power).

Thankfully, coils don't lock on very often and are protected by fuses when they do.
The actual wattage of resistor you need depends on how often the coil is pulsed and for how long.
As long as the resistor is allowed to cool between activation cycles then you're covered.

The hard part is figuring out the wattage value for the resistor required for these pulse overloads. There have been studies done on most resistor types for pulse overloads but I have never read them so can't go any further on that one.

Many resistors have a pulse overload test performed by manufacturer. This pulse overload test is typically performed at 4x rated power and typically at 1 second on, 25 seconds off. Coils are typically on for only milliseconds at a time with more than 25x inactive gaps between. My seat of pants guess would be that a 20W part (still a whopping 10x pulse overload) would work in a properly working circuit. Locked coil and all bets are off. I would love to see how many pieces a quarter watt carbon film resistor would burst into if this was tried.