A common reason for short cycling is having a boiler that is way oversized for the structure. A second reason is if the thermostat is located where it can be influenced too quickly for a local change, i.e., it's near a heat source and is sensing that versus the general room temperature.
On a boiler, there's usually a min/max. The boiler usually heats up to its maximum, then turns off, while waiting for things to cool off, and if it gets that far, turns on again. On many, this is an adjustable range. If that's too small, it will quickly hit the high limit and shut off. If you have the system zoned, and only one zone turns on, if the amount of radiation is too small, it can't dissipate the heat from an oversized boiler, so the temperature rises quickly, and when it reaches its high limit, it shuts off. Ideally, the boiler would be sized so that it can just produce enough heat to match the heat lost to the outside, and thus maintain the desired setting. THat rarely happens since the outside isn't a constant level, and solar and wind effects will also affect how much heat is gained or lost, in addition to how well the home is air sealed and insulated.
If the actual sensing devices are not working properly, that can cause the boiler to shut off. Does the boiler actually fire properly, and if so, how long does it stay on? What temperature does it get to?
So, without some more info, it's really hard to help. Need more info on what radiation is available, the actual boiler in use, where in NY you live (zip code is enough) and maybe a picture of your heating system.