I have a two story house, 12 years old. Temperature upstairs is five or six degrees hotter in summer than downstairs.

Would a variable speed A/C help? The air coming out of the vents is very cool. The problem is air flow volume to the 2nd floor.

Variable speed will not help at all. The problem is your duct system. You will have to make expensive changes to the duct system OR install a separate unit for upstairs to correct the problem. If anyone tells you different they are not telling the tuth.

You can try to crank your blower fan to a higher speed but then all the humidity will not have enough time on the coil to be removed. Your house will feel damp.

Sometimes you can close off some of the dampers in the lower level forcing more cfm to the upper level. If your duct work isn't big enough, it will be a lot noisier. I usually prefer to install a second unit for just the second floor. You can run it only when you need it and not have to operate the main downstairs unit as hard.

There really isn't a "cheap fix" for this problem, you will either have to install a separate system for the upstairs or install a zone system, the zone system would allow you to have a little more control over the upstairs tempature. Is the system sized properly to cover the upstairs?