When doing a couples return, what decides who gets the GST credit and climate action incentive?

Automatically goes to the person whose return is processed first. 

https://www.canada.ca/en/revenue-agency/services/forms-publications/publications/rc4210/gst-hst-credit.html

About the only way to "designate" who gets the credits would be to netfile or mail the second return a few days after the first.