Question pretty much says it all. I'm installing a sprinkler system in the yard, and discovered the pressure is too high (valves were leaking when on, and kick when turned on/off). I can see whichever device comes first reducing the work of the second device, but I expect it's the potential failure cases which would make it matter if one came before the other. If it matters.
I say BFP first.
The backflow preventer must be installed before any point in the system where the line becomes "open" to the introduction of pollutants that would make the water unsafe for drinking (fertilizers, pesticides, herbicides, animal wastes, bacteria, and other things you generally find in your topsoil). While a pressure reducer's basic operation (most are similar to a gas regulator, where a spring-driven piston controls an inlet) is generally "closed", most designs also have overpressure reliefs that vent liquid from the regulator in cases where the "downstream" pressure becomes dangerously high (freezing temperatures, or conversely overheating). This relief valve opens the regulator (and the water in it) to the introduction of pollutants, and so it must be "downstream" of the backflow preventer to safeguard the potable water supply.
Now, as SteveR said, if the pressure reducer is designed and intended to regulate the pressure to the entire water service (reducing the pressure from the mains to a safe level for home plumbing) then its design will ensure that it cannot introduce pollutants in any situation (usually it won't have an overpressure relief) and so it's safe to place in front of a sprinkler backflow preventer. However, if this is a reg for sprinkler systems (i.e. drip irrigation) then it must come after the backflow preventer for the system.
I would think you would need the backflow valve first. I don't think it maters much for operating, but I think the water co. might want it that way.
Are you regulating the water pressure to your whole house? Or just the irrigation system? I ask because if you are doing the house, then you need to adjust the air pressure in your expansion tank on the water heater if you have one. The air pressure in the tank should equal the water pressure from the output of the water regulator.
On service protection pressure regulator should be first if you have high pressure ie:above 100psi I've installed 10 backflows at lake level with tanks being at least 500' higher Over night during low usage pressures at BACKFLOWS increased and actually blew out the washer on the relief valve Some of the washers actually dis lodged from the Backflow and we're laying on the ground So needless to say I thought I was a champ after the installs All to get a call the next morning that all the devices I installed were in full port discharge