Externally Power an LCD

Azinman is right, get a 5v regulator, throw in 10uF decoupling electolytic capacitors between the input 9v and gnd rail, and the output 5v and gnd rail, and you have yourself a nice, smooth 5v power regulated supply.

for a better descrpition, read "step 2" of this lesson:

http://itp.nyu.edu/physcomp/Tutorials/ArduinoBreadboard