Hooking up LCD without potentiometer
In figure 2, page 7 of this document, it suggests using a 10K to 20K pot between Vcc and GND, so you might try using some 5k resistors to create a voltage divider that you can tap off of:

    Vcc
     |
    5k
     | (tap here)
    5k
     | (or here)
    5k
     | (or here)
    5k
     |
    Gnd


Try connecting the contrast input to one of the connections between the various 5k resistors and decide which gives the best result.

If you don't have 5k resistors, most any value 1k or above should work, as long as it isn't drawing too much power from your supply.