You could add a resistor and make a '24V' relay, however it will draw about twice the current as the original relay. This is not a good idea- the rest of the circuit may not function properly and cause other problems. These parts are not particularly expensive- suggest you get the right part. Pay attention to the current rating too.
By the way, the designer of that PCB was most likely operating in an extremely cost-constrained environment. That they chose to use a 24V relay rather than a 12V relay tells me that they were likely using a dropping capacitor supply and had to use a lower current relay to keep the size and cost down- so your 12V relay + resistor is likely out. In massive quantities the 24V relay will be slightly more expensive than the 12V relay because the coil requires more turns of finer wire. Usually 12V and below are the minimum cost parts.