A 1993 Miata also came with a factory air conditioning system that utilized R12 refrigerant, which is currently unavailable as it was discontinued in the 1990's.
The system most assuredly has been modified / retrofitted over the years to accept R134a refrigerant.
If this was done properly, it would allow for years of trouble free operation. It is true, however, that R134a in a system that was originally designed for R12 refrigerant can underperform in general. And, there really is nothing that can be done to make this better.
As Pushrod said - diagnostic testing hands on is really needed to evaluate the functionality and operation of the system as it is right now, and determine if there is something not working properly or perhaps there is a leak in the system somewhere causing refrigerant loss.
RepairPal Certified shops can diagnose and repair your 1993 Mazda Miata. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.
Keeping the convertible top up while a/c is operating will help ,