I have just replaced the thermostat with a new honeywell CT31 to see if
it makes a difference.
Thus far the last 20 minutes the system is cycling on and off about
every 2 minutes.
It is 42 degrees out right now.

You mentioned to change the anticipator setting. This model has
something
some adjustment which I assume is what you mean. I set it to 0.4.
Are you recommending I change it 0.8?

Is this the temperature drop at which it turns on or when it turns off?

gas/oil furnace 0.4
electric furnace 0.3
high effic. furnace 0.8
hot water 0.8
gas/oil steam system 1.2