I was just up there today (Florence Junction). There are two ways to get to the Coke Ovens, from the North or the South. The South Way is easier, but the North way is a lot more fun.
To get there the North way you drive south about 5 miles from the intersection of US60/AZ 79 and make a left at a flagpole. This is the route for Martinez Cabin. It's very easy to get lost around this area and I hit the Woodpecker trail by accident. Didn't take me that long to figure it out once I approached 3 foot boulders.
Anyway, you keep going on Martinez Cabin trail and you eventually hit the turn off for the Coke Ovens trail. When you come back from the Coke Ovens you can go south through Box Canyon and eventually hit AZ 79 and go north back home.
I'm not sure if a stock 4Runner could make it through without relying on skid plates and/or rock sliders. I don't have either but do have a 3/2 lift and 32" tires. I knocked my gas tank skid pretty decently but that's what it's made for.
This is me accidentally going on Woodpecker and scurrying back with my tail between my legs. I was wondering why all of the ATVers were looking at me funny.
This is the hardest part of Martinez Cabin, it's pretty unnerving driving it for your first time. But it's actually not too hard.
Another shot of my climbing down the ledge. My passenger side rear tire is actually about a foot off the ground. Gotta love that feeling when your truck starts to tip.