A mix of different things will give the best cover and erosion protection.
The things to look for obviously are
deep roots and shading out of unwanted volunteers.
clovers, hairy vetch, buckwheat, lupines, Sainfoin, mints, marigolds, etc. would not only do the job needed,
but they would also give back with flowers, no need to worry if dogs go crazy on the slope, all of the above will
reseed and or are perennial in nature, don't really need any care either.
even some herbs such as rosemary could be good additions to a mix, then you have a bonus of plants that deter ticks,
fleas and other nasty dog loving bugs.