You can power your ardiono from a 9V battery. Actually the Arduino has a voltage regulator that allows you to use a range of input voltages.
Even 12V is possible, but not recommended. If the beacons should run of, lets say, 12V, then I would just take those 12V, but in a voltage regulator 12V->9V and run the Arduino of that.
The advantage is that you never need to change the battery.
There are also other voltage regulators that allow regulation to 9V from higher voltages (in case the beacons run at higher voltages).
Popular voltage regulators are the LM7809 series (just google for them).
The Arduino usually uses so little current that one beacon power supply should have no problem to power beacon and Arduino.
here is a picture of a potentail setup. really just a rough sketch.....
basically you cut ther + from the beacons and wire both to relays. those relays get switched by the arduino.
On one power supply you also hook up a voltage regulator that powers your arduino. the ground of all devices must be connected.