To avoid damage to my 2 foot underground water pipe, I need to blow
the water out before the ground freezes.

Pipe Length = 150 Feet
Pipe diameter = 1 in.
# of outlets = 2
Outlet sizes = Garden hose size

Compressor Output goals -
Minimum pressure desired = 5 psi
Maximum pressure = 50 psi
4 hour continuous.

Question:
What size air compressor CFM and tank do I need, to accomplish my goal?

Thank You

Fortunately this is not an answer. It is just a comment to pump in
some interest on your question. If this comment sucks, feel free to
blow it away.

Do I understand that you want an air compressor to blow out the water
in your 1-inch diameter, 150-ft long pipe system that is buried 2 feet
below the ground before the ground around it, and so the water inside
the system, freezes?

a) Is that the practice in your neighborhood? If so, why not ask around there?
b) Since I have not been to a place where it snows, does water in
pipes freezes, 2 feet underground or not, in your kind of place? If
so, how do people in your kind of place get water from their taps?
They don't? They melt snow instead? They buy water from stores?
c) If water is removed so that it won't freeze inside the water pipes,
do the hollow water pipes not break at the joints when they are frozen
eventually?
d) Why, if water is not removed, do the water pipes break at the
joints when they and the water inside are frozen eventually?
e) Say you need to blow out the water for whatever reason, when are
you supposed to do that? Do you monitor the temperature around the
pipes the whole length of the system underground? (Improbable, I may
say.) Do you monitor the temperature of the water that comes out of
the pipes? That when the temperature is about 35 degree Farenheit or
about 1 dergree Centigrade, you start the process of getting rid of
the water inside the system?
d) You do that every winter? 

Probable solutions:
1) Like I said, ask around your neighborhood. Someone might even sell
his air compressor to you flea-market price (because he's leaving your
place for he's tired of the ritual finally).
2) If your system doesn't require big pressure to blow out the water
through the two outlets, try blowing through one end/outlet using your
mouth. If you practice or play with a trombone or tuba or bagpipe,
that should be easy.
3) If you cannot do the job with your own power, try next with a
bicycle air pump or baloon air pump.
4) If those won't work either, try with the ordinary 3 to 4 CFM @ 90
psi air compressors that contruction workers use with their air tools.
Those compressors are strong enough. Should be strong enough to do the
job.
5) If those won't work also, I suggest you just let the water remain
in your system. Cross your finger that the frozen water will thaw
eventually without damaging anything in your system. And pray too.

Remember, it is only  1-inch diam by 150 ft long. Short. Not much
water to in them there pipes. About 6 gallons only.
Which brings out why you need 4 hours continuous pumping? It should be
done in less than 5 minutes only, I guess.
Just don't forget to disconnect your system from the water source.
Close the gate valve at the entrance/beginning of your sytem. And open
all the other valves after that so that the ventilation is free for
the water outflow.

Since I don't know the horizontal and vertical layout of your system,
for gradients, waterhead, static pressures, whatever, I cannot make
calculations.

------------
Or, is your pipe 2 feet in diameter? If yes, what kind of business you
have there? An atomic reactor?
An 8-inch diameter water pipe main can sustain a large village!

Here's a link that discusses the variables affecting:

[Depth of Ground Freeze]
http://www.newton.dep.anl.gov/askasci/env99/env266.htm

In any case, I think I'd trying draining the hose with a water-proof
shop vacuum, e.g. Sears' "Wet-Vac".  If the 1 inch diameter, 150 foot
long pipe were completely filled, the contents amount to less than 8
gallons.  It shouldn't take more than a few minutes to drain, and if
it were convenient to position a garden hose extension end more than 2
feet below one of your outlets, you wouldn't even need the shop
vaccum; just establish the siphon and let gravity do the work.  If you
ever drained a waterbed this way, this will likely be an easier job.

regards, mathtalk-ga

Kidding aside, if your concern is that your pipes might be damaged due
to the expansion in volume of the trapped water if frozen, then try to
remove at least 10 percent of the water. No need to drain the whole
thing.

Let us see. 
Density of ice is 0.931 g/cc. Density of water is 1.00 g/cc. Meaning,
for the same weight of water, volume of ice is 1.074 times the volume
of liquid water. The volume of water in your 1-inch diam by 150 ft
long pipes is 6.12 gallons. If that will freeze, the volume will
expand to 6.57 gallons. That is about 0.45 gal more than the volume of
your pipes, 6.12 gal.
So you need to free at least 0.45 gal of frozen water. In terms of
liquid water, that will be about 0.42 gallon.
Meaning, you need to remove at least 0.42 gal of the water before it
freezes. Say, half a gallon. The remaining water can then freeze
inside your system without exerting additional pressure against the
pipes other than its weight.

a) By whatever way, get out at least half a gallon of the water,
depending on your enthusiasm. A half-gallon jug at the outlet will be
good for measuring the outflow.
b) Or, just let the outlets kept open. The excess water will drip out
as the water freezes inside the system.