The only "center" type constraints are for round type objects.
Your options for square peg in a square hole are: (from my most preferred to my least preferred)
1. create a axis at the center of the square peg and at the center of the square hole and select those. you can create an axis in the sketch by adding a "datum point" in the sketch and using construction lines to keep it centered on the sketch.
2. if you already had datum planes at the centers, you can use the datum planes to assemble.
3. use a distance constraint to hold a surface of the peg at a distance from the surface of the hole.
(2)Use the Edit definition button, select the component you want to redefine, RMB, it's the orange-ish ball with a pencil looking thing...I've never understood that visual.
If it's indeed a square push button which can translate up and down when activated / deactivated, I would actually suggest using a Slider mechanism connection. And as suggested, you should create the push button and the square "hole" with axes down the center for Axis Alignment of the Slider connection.
Here's a video that has a Slider connection: https://youtu.be/J_YNvWWA13E
You could then use Mechanism Snapshots to capture the different positions of the button.
Hope this helps,