If you have a Server and you don't want to install Essentials for one reason or another, you can use this SimpleMessage plugin to allow private communication between players very simply.
This plugin is extremely lightweight and simple to use.
There are no permissions involved as all players should be able to use the command involved with this plugin.
The only command that exists is:
/msg <Player> <Message>
Which is the normal usage of the msg command used in Essentials.