Can I put an automatic convertible top on a car that originally had a manual one.?

Just as with the manually-operated roof on the Mazda MX-5/Eunos/Miata, it’s not really a viable option. 

The roof itself would need a total redesign from scratch, and the car itself lacks the spaces needed to fit an electric or an electrohydraulic motor plus all the sequencing microswitches.

Custom-made roof mods of that kind also tend to be pretty unreliable. 

The modifications would cost more far more than the car is worth and would need to be declared as a modification if you have insurance to cover your own car against damage.

If you want a powered soft top get something like a Boxster 986/987. You’ll then be getting a much better car in terms of styling and practicality (not reliability or economy though) as the 986 is what inspired the design of your MR2.

If you buy a 986 then make certain it has has the IMS bearing modification or budget to get it done immediately. The 987 is a face-lifted 986 but also does not have the catastrophic risk to the engine of IMS bearing failure. It also has a far less failure-prone AOS than the 986. The Air Oil Separator is not a hugely expensive part but it is an utter swine to replace and on the 986 it rarely lasts more than 2 years before failing again (producing huge clouds of smoke from the tailpipe).