I would really be surprised if the GPS input requires a relay. More likely, it wants isolation that a relay might provide. If you are using an opto-isolator, you may be able to interface your opto-isolator output directly to the GPS input, in which case your problem becomes more about driving the input of the opto-isolator.
What specs can you find about the GPS inputs? Voltage levels? TTL? CMOS?
Is there a spec on the output suggesting it comes from a CMOS output, or is it from a sensor that has an open-collector, open-drain, pull-down only type of output? If might say something like "sink current=Xma"? Possibly "source current= YmA"?