In general a "regular" residential contractor would not "build" something like that. What you could find is a contractor to install a lift system that is designed and engineered for that purpose. Even then, there can be a variety of building codes, safety codes that might be expensive to meet, if you have them.
My point here is that rigging something up yourself that will do the job (meaning you accept liability) is probably a very different price point than hiring a company to install a lift system and accept the liability.
I have seen people use an automotive lift to lift motorcycles on to a mezzanine, but that was not as high as a second floor. Some lift companies make high rise lifts that will clear a motor home if you have the space. You could call a few lift companies and get so info from them if that is within your budget.
Regardless of what you use to lift the motorcycles, you need an opening either in the floor to the second story, or on a outside wall of the second story (like old barns did) for access to the 2nd story.
I think the most economical way to actually lift the motorcycles, would be to buy a used fork lift or Genie type lift that would do the job and take up less space in your garage, if it is for seasonal storage only, you could just rent a lift twice a year for that matter.
