Is there a way to get the gripper to open by a digital input(a button)? Say after you stop the program when the gripper is closed, is there a way to wire a button to an input that would open the gripper when pushed?

On which robot are you working ?
The usual way to open the gripper is to write gripper register using Modbus RTU.

Ur5. 

You can use the top menu on the teach pendant to open or close the gripper when no program is running.



Control over IO may be possible if your gripper is connected on a UR CB Serie via a Robotiq IO coupling.

I am looking for something like how you can assign the freedrive to an input, but for gripper open.

To open the grIpper you have to execute a program on the robot.
It is a bit complex but you I think you can have a arduino like system with a program monitoring a button and send a command via robot interface to open or close the grippe.