A disparity in the temperature between floors is common in poorly designed HVAC systems. Heat rises and so the second floor will tend to be hotter than the first, all things being equal.
If capacity wise, the system is able to handle the square footage of the home, your best option might be zoning the second floor separately from the first floor. This is a modification that can typically be added to existing systems.
If the existing system is insufficient or 'on its last legs', you might need to replace what you have. In that case, the best solution would be 2 separate systems, or a larger capacity one with zones.
Good luck!

I bet that your existing air handler is in the basement and is trying to cool both floors. This system rarely works unless it has a separate zone for each floor. This will allow the 2nd floor to run much longer cycles than the 1st floor for cooling.
The 2nd alternative is to install a 2nd cooling system that will be dedicated to cooling the 2nd floor only.