It is possible to use SSH to encrypt the network connection between clients and a PostgreSQL server. Done properly, this provides an adequately secure network connection, even for non-SSL-capable clients.
First make sure that an SSH server is running properly on the same machine as the PostgreSQL server and that you can log in using ssh as some user. Then you can establish a secure tunnel with a command like this from the client machine:
ssh -L 63333:localhost:5432 email@example.com
The first number in the -L argument, 63333, is the port number of your end of the tunnel; it can be any unused port. (IANA reserves ports 49152 through 65535 for private use.) The second number, 5432, is the remote end of the tunnel: the port number your server is using. The name or IP address between the port numbers is the host with the database server you are going to connect to, as seen from the host you are logging in to, which is foo.com in this example. In order to connect to the database server using this tunnel, you connect to port 63333 on the local machine:
psql -h localhost -p 63333 postgres
To the database server it will then look as though you are really user joe on host foo.com connecting to localhost in that context, and it will use whatever authentication procedure was configured for connections from this user and host. Note that the server will not think the connection is SSL-encrypted, since in fact it is not encrypted between the SSH server and the PostgreSQL server. This should not pose any extra security risk as long as they are on the same machine.
In order for the tunnel setup to succeed you must be allowed to connect via ssh as firstname.lastname@example.org, just as if you had attempted to use ssh to create a terminal session.
You could also have set up the port forwarding as
ssh -L 63333:foo.com:5432 email@example.com
but then the database server will see the connection as coming in on its foo.com interface, which is not opened by the default setting listen_addresses = 'localhost'. This is usually not what you want.
If you have to "hop" to the database server via some login host, one possible setup could look like this:
ssh -L 63333:db.foo.com:5432 firstname.lastname@example.org
Note that this way the connection from shell.foo.com to db.foo.com will not be encrypted by the SSH tunnel. SSH offers quite a few configuration possibilities when the network is restricted in various ways. Please refer to the SSH documentation for details.
Tip: Several other applications exist that can provide secure tunnels using a procedure similar in concept to the one just described.