If you are asking did honda make a 1977 atc with a 110 engine, no they did not. If you are asking can you fit a 110 engine in a 1977 frame, yes you can. Comapnies at one time made components to build up a stock atc90 into a 183cc engine, or roughly there abouts. But, those high performance components were expensive during their time and even harder to find and more expensive now. With enough money and modifications, you can even put a 200x engine into an atc90 and there are also larger displacement engines that were built, but the technology is very exotic compared to what a stock 90 or 110 engine is. I'm not sure why you are asking this question?
Nicholson 500x (Project)
Nicholson 185s
Nicholson 110 (That takes an atc70 tank)
Ascott 500 head/350x (Project)
Homebuilt Racer Chromoly Suspension 110 (Ragin Runt)
PK Racing Suspension 70
A+ Inc Suspension 70
AWS Aluminum 90 frame
Hi Performance ATC Suspension frame rd350
Hi Performance ATC Suspension frame 90