Even turbinado sugar will work in a pinch.

Muscavado sugar is closer to palm sugar than other sugars.

Light brown sugar

Here's a great source of information about substitutions of sweeteners: http://www.foodsubs.com/Sweeten.html . ;o)

Measure the brown sugar, pack it down, allow it to dry and harden and it's almost indistinguishable from a block of palm sugar. To use it, grate it into your recipe or melt it with a liquid. Or you could check an Indonesian or Thai grocery for coconut sugar (the sap from the coconut palm, not because it tastes like coconut).

Light brown sugar