I plan to install a sewage ejector system in the basement for a new bathroom.
The problem is finding a route to run the 2" vent from the ejector pump system to the roof. I am unable to find a way to get the vent up through the
Existing home to the roof. What other way,if possible, is there to vent this
System so that it is properly vented ? Thank you for any help you may be able
To provide.

I don't know your intentions but if you plan to get a permit and an inspection I would consult your city plumbing inspector. I am sure if you told him you were going to do it yourself he would give you some insight on how would be the best way.

I know that in the state of Texas you can do you own plumbing if you are the home owner and it is your place of residence.

Since a sewage ejector system vent both pulls air in and vents it out a AAV(Air Admittance Valve) cheater vent may not be used. However,
Sections 1404.4 and .5 Of the Standard Plumbing Code, (Extensions Through Wall) allows you to extend vent terminals through a wall providing that,
1- No vent terminal shall be located directly beneath any door, window or other ventilating opening of the building.
2- No vent shall be located within 10 feet horizontally of such a opening unless it's at least 2 feet above the top of such opening.
Now you have options. Good luck, Tom