Increase voltage and current with external power supply
It sounds to me that with a limited ability to drive current to the relay you are currently using you have two options: -


Choose a relay that takes less current (maybe an opto relay or SSR)
Use a MOSFET (that can be driven from the IO line at low current) to connect the relay coil to 12 volts. Don't forget the flyback diode of course.


The 2nd option would require an N channel MOSFET interface like this: -