If the system cycles off/on a lot, its usually an indication that the system is low on charge, most likely from a leak. I've seen this a lot with older cars that have been converted, if the conversion was not done right, there could be multiple small leaks, but if there is dye in the system, you could use a UV light & yellow glasses to trace down the leak and/or an A/C system sniffer, but those can be expensive.
On a side note: The R134a is a conversion, not really considered an upgrade on a system designed for R12. An R12 system with R12 will always blow colder than a R12 system thats been converted to R134a.