I'll assume that you'd be using hand tools, meaning a shovel.

Under optimal conditions, where the soil is slightly moist and very gently compacted, you can probably remove dirt at a steady pace of 5-10 cubic feet per minute, taking an occasional break. So it should take you about a half hour, with this and that. Possibly 15 minutes if you dig like a madman...or maybe a sane man with your life on the line. If you've got more than one person you can make things go a bit faster.

Generally, conditions will not be optimal. If the soil contains many rocks larger than pea-sized, or if there's a lot of moisture, or if the soil is sandy, or if it's heavily compacted, and so on and so forth. Given that the soil is somewhere that people decided to bury a casket 6 feet deep in the first place, I think that you can assume that it shouldn't take more than a day to excavate unless it's a really old gravesite. There shouldn't be great big rocks (unless deliberately placed as protection against grave-robbers), the soil will have been broken up once, it shouldn't be all that sandy, and so on and so forth. But realistically, conditions will generally be non-optimal and you'll spend a couple of hours digging that big a hole.

There's also the question of removing the casket itself (if you're including that step). How much longer this will take depends a lot on the casket. Your casket of a bygone era was intended to fit the body pretty closely to minimize the amount of collapse once the casket rotted. Modern caskets are often the size and weight of a small piano (once the body is inside) and are supposed to be virtually indestructable, to the extent that you can excavate them with a backhoe without worrying about chopping the corpse in half.

The story just has one character digging up a grave in the middle of the night, a grave that was just filled in earlier that day. The story is set a little south of a post-American Denver. I had him taking 30 minutes to dig 7 by 4 section, about one foot deep.

Of course there was a grave digging scene in Magic Street. Seemed to take 10-15 minutes. But they were digging like someone's life was on the line.

Anyway, if the story is "post-American", then I'd guess that the whole indestructable, hermetically sealed casket thing has also gone out of fashion. We're probably talking about a disposable pine casket, like in old times. That means that you don't need the hole to be 7x4, the digger can just dig down towards the torso, break open the top half of the casket, and slither the body out. The hole still has to be about three feet across for him to have a decent amount of room to use his shovel, but it's a lot less dirt than 7x4 (if the story is post-American, I wouldn't count on the initial hole being that big either).

Also, when a grave is freshly filled, it is common practice to heap a mound of earth over the grave to offset settling. This mound should be at least a foot high for a 6 foot grave. You can remove that in under a minute if you make a speed event out of it (a couple of minutes is more reasonable). The layer underneath is almost as easy, very lightly compacted and you still have an advantageous angle. Digging gets progressively more difficult the further down you go. The soil is getting more compacted, you're further down in a hole so your movement is restricted, you have to worry about getting the dirt out of the hole (after you get about waist deep it's best to use a bucket for this), dirt dislodged from the sides of the hole starts becoming a problem (less of a problem in a pre-dug hole, but still noticible), and you'll start to get tired of digging.

I'd say that overall the rate of progress has a bit of a square function...that last couple of feet will take you as long as the rest of the hole did.

Lived there. Did that.

Inkwell
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"The difference between a writer and someone who says they want to write is merely the width of a postage stamp."
-Anonymous