I bought a cat genie. It pumps the liquified cat___ into an open toilet bowl or into a washing machine drainpipe.

I do not want to put the cat genie in the washroom and use the same drainpipe as my laundry wastewater does.

I want to add a second drain pipe about 8 feet away(downstream) into the 6 inch dia (thats a guess on the diameter) main sewer pipe (pvc) that wraps around the perimeter of my basement.

I don't want to cut a section completely out of the main sewer pipe and add a coupling t
(that is the obvious way and is the way the laundry drainpipe is installed

Is there a way to drill a 2 inch dia. Hole and glue on a coupling that wraps around half the pipe to add this second drainpipe?

You might wish to reconsider the washer stand pipe when you hear what you'll have to do to install a second stand pipe.
I know of no saddle clamp coupling in any size that you can install on the main. But that's just the start of your problem. You will have to cut into a stack or open up the floor to cut a fitting into the main. Next, it will have to be trapped. In addition you will have to run a vent out the roof or revent back into a existing dry vent in the attic although, id local codes permit, you could install a AAV,( Air Admittance Valve) in place of a regular vent.
Regards, Tom