suggestions for hardy grass alternative

I have four dogs and a relatively small yard.  Every year we make a futile effort to grow grass over the dirt trail that the dogs make as they bolt from the back door to the fence line when we let them out.  I'm hoping someone might have a suggestion or two for a hardy grass alternative that can stand some heavy traffic.  I don't care what it is is, I'd just like to have a green yard again.  (Conversely, we've also considered laying stone over the trail but that seems like an awful lot of work...)  Thanks in advance for any help!

To start with, we need to figure out if we are looking at a warm season grass or a cold season grass.

How cold does it get at your house?

The coldest average month hits in the low 20's.... The summers are always hot and humid, and often DRY.  We did ok with getting some grass growing last year, then had it all wiped out in the drought.   Also, the yard gets fairly saturated in the spring- between the thawing snow and spring rains- we get a lot of run-off then because our house is located near the bottom of of hill.  More info than you asked for, I know, but I just thought I'd throw anything that might be helpful...

You need a cool season grass.

I suggest "tall fescue".  You can get a mix of different tall fescue seed, but do NOT get mix of tall fescue and something else (like ryegrass or bluegrass). 

Tall fescue is famous for use in playgrounds because it is so durable.  It is also famous for all sorts of other things which make it excellent for organic lawn care.

Thanks, I'll try it!