The pin in the upper back door hinge is broken.
Is there any DIY fix to this?

 

I'm not a fountain of knowledge by any means, but it looks like the hinges are just simply bolted to the door. You should be able to unbolt the entire hinge and replace it with a new one.

 

I agree with Rover Curious and I would replace both hinges, upper and lower due to the stress placed on the lower hinge after opening such a heavy door with spare tire to boot.

You would have to spray paint the hinges prior to mounting them. I have had good luck getting an exact match paint in a 12 ounce spray can from carquest parts stores (You just give them your paint code and they will make a can for it). Not sure if you have them in your area.

 

Thanks guys.
Unimoged, do you know the code or at least a link where I can find the paint code for alpine white?