How to I enable jumbo frames on just one network interface?

The question is phrased like there's a way to globally turn it on. I'm not aware of that method, here's how I'd turn it on:

sudo ip link set eth1 mtu 9000

Or (as this is a server) if you're using the /etc/network/interfaces configuration, you can simply stick it in at the end like so:

auto eth1
iface eth1 inet static
        address ...
        netmask ...
        network ...
        broadcast ...
        gateway ...
        dns-nameservers ...
        mtu 9000

I suggest you test the MTU rate with ip before you persist it in /etc/network/interfaces. Oh and you'll need to run sudo service networking restart if you only used the second method there.

You can verify the configuration with ip:

ip link show eth1

And there are various things like traceroute --mtu that can measure and test that MTU.