What size cable do I need for a replacement sub-panel?
For 70 amperes, you'll want to use 4 AWG copper or 3 AWG aluminum conductors. If the run is overly long, you'll want to compensate for voltage drop, by increasing the size of the conductors.  

It looks like there originally wasn't an equipment grounding conductor included with the feeder, but you'll need one with the new feeder. If the original feeder was run through conduit, you might have to upgrade the conduit to fit the additional conductor.

If the original feeder was a cable assembly, and not individual conductors run through conduit. You should be able to replace it with 4-4-4-6 cable, from the local big box home improvement store.

When you install the equipment grounding conductor in the new panel, you'll want to make sure the neutral bus bars are isolated from the ground. And you'll have to terminate all the neutral and grounding conductors at the appropriate bus bars.

NOTE:


If you're replacing the panel, you might have to install AFCI and GFCI protection devices as required by code.
If you don't want to rewire all the circuits in the panel to add a grounding conductor, you might want to consider adding GFCI (and possibly AFCI) protection devices.