I'd say in cases such as this, styrofoam is your best friend.  You can build a general structure out of lumber, and then skin it with styrofoam (or even skin it with lauan, and then styrofoam that if you want a little extra support). 
When working with styrofoam, attach it using white glue!   Just using screws won't cut it.

I usually white glue, and then use screws with sizeable washers on them (so they grab more of the surface), being very careful not to go too far into the foam.  That provides a pretty sturdy anchor while the glue sets.  Painters tape will cover the spots where your fasteners are.

Once the styrofoam's all on, you can use spraypaint (it makes the styrofoam melt) to rough it up a bit, for a realistic stone look. 

It'll work for the crate too, using strips of foam for the crate's crossbeams and such, and will be much lighter as a result.

That handles the construction end of things, the rest will come from paint.  Just get familiar with rags and sponges, and google can help you find methods to create realistic stone and wood-grain textures.

As an alternative to spray paint.. you can use gray stone colored latex and mix in sand to the desired consistancy and this not only produce a predicable finish but it dries pretty quickly and makes the styrofoam tuff as heck.  I used this all the time for headstones, and other stage stone components.

Do me a favor, if you get a coffin, tell the actor it is new.  I once was given a beautiful suit to wear as the Gov. of Texas in Whorehouse.  When I asked where they got the suit they were very vague.  I later found out they borrowed it from the Producer's brother who runs the local funeral home.  He has a whole rack of suits for the corpses who dont have anything nice to wear.  They put them on for the viewing and then take them off before the burial.  They swore it had been dry cleaned but I still get the creeps thinking about that suit.

There's also this link here:  http://wayneofthewoods.com/coffin%202.html

Coffin plans!   You can substitite a less expensive plywood... this is for a pretty professional finish, like you'd find in a bookshelf.  For stage purposes, you don't need the whole 3 sheets of plywood he calls for.  I'd just use the template to get all the dimensions and angles correct.  I also recommend some foam in the bottom, for comfort.