Can a Garmin Touring charging port be repaired
As long as the unit is not fully sealed and the port is accessible then yes, the port can be changed. Changing the port is not a job just anybody can do, as in a lot of cases these days just like with mobile phone repairs experience in micro-soldering may be required especially where the ports contacts are soldered to the PCB. 

Hot air stations are normally used on this sort of job as the port is usually soldered to a PCB ground plane which makes removal with an iron alone virtually impossible.  

A mobile phone repair specialist will likely be able to replace the port for you.