Your question is confusing - you are asking if there is a more efficient way to COOL the building and yet you are talking about boilers and steam lines/radiators. The steam and radiators are used for HEATING. So basically it sounds like the occupants are using the steam system for heat and window A/C units for cooling - what exactly are you looking to do? Are you looking to replace the HEATING system or install a COOLING system for the whole building?
Also, you have to answer this question: how much money is willing to be spent? There are many efficient ways for climate control. Steam is generally a pretty good way to go for heating but I'd say in a building that old it could definately be improved.
If you are looking to install BOTH heating and cooling the most efficient method is probably going to involve the use of ground water. Either a system of ground source water to air heat pumps or ground source water to water heat pumps and fan coil units in the building. However, systems like these require a sizable investment up front to install (in other words it's expensive as hell) and you would need the ground space outside to install a well field. But after installed the system would use water from the ground YEAR ROUND to provide cooling in the summer and heating in the winter. If set up correctly these systems can also provide "free cooling" during warm days in the spring and fall (when the ground water is cold enough to cool the air directly, without the need for the heat pump's refrigerant cycle to be operating).
Give me some more details on exactly what you are trying to do and I can give you more specifics.