A 1N914 can safely handle 200mA continuous. Most 12V relay coils draw much less than 200mA. Surge current ratings are much higher, but without knowing the relay switching frequency, I would use 200mA as a maximum.Usually diodes are inserted that way to absorb inductive kickbacks, which can damage drive circuits such as transistors. When a coil goes from full current to none, it generates a reverse voltage and current, sometimes pretty substantal. Just as a capacitor can generate a high current trying to maintain a voltage through a short, a coil can generate high voltage trying to maintain current through an open.
Only thing that is off is generally a power diode is used, instead of a small signal diode.
Coil current is only 60mA. The 1N914 will work for you.I am using it as protection for spike,
the relay is this: 12v 5a.