I'd do as flags says, aiming for the middle of the chest, but I would think that if your only opportunity is on the back end of your range (60 yards, you say), you should avoid any quartering shots and only attempt broadside shots.
If all you can do is cover a pie plate and know it'll land somewhere therein, you don't want to risk gut-shooting or brisket-shooting a deer because it presented you with a narrow target.

I would just keep my shots to 60 yards and aim in the middle then.

Shouldn't be a factor at 60 yards

^What he said.^

I know you said you can't afford more equipment but my suggestion would be to replace your front site (dunno what you have on there now but it sounds like it's too big) with a smaller front site. And maybe replace the rear with one with a slightly larger aperture. Not a great expense if you shop around. Or learn to shoot using a 6 o'clock hold rather than dead on covering your target picture. Either one will cost you about the same. Slugs aint cheap so learning to hold 6 o'clock will cost you a good little bit. Kinda 6 of one, half dozen of the other there. A lot of muzzleloader shooters out there using traditional equipment had to learn to use 6 o'clock hold for the very same reason. It would also help a bit if you told us what model shotgun you are using so we may be able to help you to find the proper rig at a reasonable price. Never know, one of us may accidentally have something laying around our shops that would be perfect for you! Lot of us on here have bins full of crap we never use but may "need" it someday!

You don't need to spend a dime. Practice with the shot gun don't you? then why don't you spend some time practicing range estimation? No such thing as a range finder when I started hunting so all the old timers said to pick a spot, a tree, bush, a car and guess the distance and then pace it off. Average pace of a full grown adult male is around 37 inches. Lot of times you don't have time to use a range finder any way. If you stand hunt you can always have a friend come and measure distances from the stand to objects.


You can also use a drill to drill out the peep sight to a larger size. just select a drill a little larger than the present hole and step up till you get the sight picture needed.


Some where I came across a chart for shot gun slugs and sighting in. It told if you sighted in at x yards you would be high this amount at xx yards and be this low at xxx yards. when I sighted in my 20ga. the chart was right on the money. Sorry don't know where I saw that chart either. Thought was chuck hawks maybe.


Al

SH gave some good advice on the 6 o'clock hold. A little head work and time on the range will train your eye to use that method. My thick woods still hunting gun is a Rem 7600 with a Williams peep and a fire dot front sight and I can hit a heart sized target at 100 yds all day. At 60 yards you should be able to be hitting what you are aiming at. If you are going to miss high or low I would elect low.

I must be misunderstanding. Are we talking about shooting 60 yards here or are you wanting to shoot further?

I know not what this, "MISS"you speak of is. but then, I do not take a shot unless I know I can make it.

practice, learn what you can and cannot do and there is no "margin for error"

If I understand the original problem that the front bead is large and covers the target thus allowing for an inaccurate shot. I believe he was worried about hitting what he was aiming for at 60 yds. ...unless I read it wrong