Any oil boiler would be insane for a house with an I=B=R calculated heat load of 14BKTU/hr. At 5-6x oversizing just the standby-loss of the boiler might be enough to heat the house most of the time (except for cold-start tolerant units.) But either way, an oil boiler is going to be a problem to be designed-around rather than a solution to a heating problem. If you go that route, only direct-vented sealed combustion units would be appropriate, since the air leakage of the vent & combustion air on other units add a real fraction to your low heat load.
Peerless makes a 0.5gph unit that might work, as well as the
Buderus Logano series, but there are fuel-quality issues that can muck with tiny 0.5gph jets and condensing oil boilers to consider too- it may be too risky to go there unless you KNOW there is the local fuel & support to run & maintain them. They're rediculously oversized for the load though.
Smallest in class propane mod-cons have a min-mod that low, and if you allow 25-50% oversizing for infiltration it might make some sense. With a radiant slab that cold efficiency could be made to average in the high 90s. A condensing propane tank HW heater like the Polaris would hit in the mid-90s, and may be the "right" solution. At heat loads that low, even at $6/gallon heating with propane won't break the bank, but it won't be free either.
BTW:
The 99% outside design temps for Block Island/Long-Island are more like +10F rather than +5F, and your heating/cooling balance point is likely to be closer to base 60F than 65F, not that it moves your load numbers enough to matter. The newer design temp listings are 4-5F higher than older listings, in part due to warmer average winter temps over the past 15 years, but also from a subtle difference in how the 99% number is defined- it's similar to what had been listed as the 97.5% number, which is a perfectly valid number to size for, particularly in tighter higher-R houses. If the place is unoccupied in winter and you're only maintaining 50-55F indoors, the heat load number will shift much more significantly.
Fuel use depends on your as-used HDD base, since your average load during the shoulder seasons drops to about zero at base 50, but at base 60 or 65 it's still a real number.