As iggsterman responded, you do not have enough available space.
Run lsvg rootvg and look for FREE PPs. You will see that you do not have enough to fulfill your request. You need to add another hdisk with extendvg or if you are using SAN storage you can simply increase the existing LUN size followed by chvg -g rootvg (g=grow). Then, you should be able to add space to the /var filesystem.