How can you mount a red dot on a Shield Performance center 9?

You can have it milled. Many choices out there mostly around $150-$160.
One Example

Sight Mount.
J&P. Vortex Razor.
EGW Vortex.
Many options besides milling. Just Google M&P Red Dot Mount.

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CERAKOTE Svcs.
Class 01 FFL

I used Lone Wolf for my Shield. The milling is about $90 and you furnish your red dot sight (Check the ones they sell to determine if they'll mill your pistol with your dot)
I bought their Shield RMS to do a Race Mill on my Shield. The mill work was excellent and I've found the Shield RMS red dot sight the best of all the ones I know about. I also chose the the one with the 8MOA dot. In short, I'm set up for SD situations. Been there.
Check out Lone Wolf Enterprises.
Stay safe
Poli Viejo