I have been out of this game for a long time now. Looking at a 33 Plymouth coupe or something to go on my 89 Dakota that’s a running 318 magnum truck. A huh I know has a 33

I know the later 30s are a good fit. Not sure about this era.

I put a 48 Plymouth coupe on a 90 Dakota frame and it worked out really well (100K miles now). I believe the 48 is a couple inches wider then the early 30s cars.
I also had a 39 Plymouth coupe with a Dakota frame, that one also cleared but were pretty close using the standard offset Mopar 7" wide steel front wheels, but I believe it too is wider then the early 30s cars.
I believe the fenders got wider on the front by 35 or 36. The 35 I built had am F,M,J clip (before the Dakota existed), but I needed to add 2" on each side for the tires to clear (they did clear easily). I believe the F,M.&J clip is wider then the Dakota, and that car used the standard off set 7" aluminum slots.

I believe the Dakota frame is going to set the tires real close to the edge of the front fenders on that 33 Plymouth coupe, even if you use the inset Dakota wheels. If you don't mind moving the front fenders out an inch or so on both sides, and don't drop the front end to the ground, it will work OK.

A picture with a good view of the 48 Plymouth tire in the front fender.
The only picture I have of the 39 is a side view with the tires turned a bit, so that won't help you much, but I'll post it anyway.
The picture of my 35 doesn't really help because everything is different.
A stock early Dakota 6" wheel has the center moves towards the outside about a full inch more then a standard factory 6" wheel, which moves the tire inward the same distance as the wheel center moved (if the wheel center moves out 1", the tire moves in 1").

Thanks.

33's and 34's are a lot narrower than one thinks, compared to the 35's and up.
only a tape measure and thinking cap will tell for sure.

This. I'm thinking the frame will be under the running boards.

i measured the frame width on my 33 dodge "humpback" delivery at the cowl, and it is only 32 1/2" wide, which although is a fabricated frame, is the stock [or very close to the stock] width.
this truck, from the box forward, is the same as a sedan or coupe, although the two door sedan and coupe had longer doors.
the stock frame is shown for reference.

I build a 39 Dodge pickup on a Dakota frame that was open wheel. I suspect it may be very close to the width of the 33 Plymouth body at the cowl. The truck is no longer here, and I don't have a lot of detailed pictures of it.

On the 39 truck, everything forward of about 1/2 way between the cowl and the grille shell was outside of the frame rails, and the cowl will probably sit on top of the frame rails, or just outside of the side rails. The grille (my bottom 1/2 of the grille shell was fabricated) will sit inside of the frame rails. The rest of the car will wider then the Dakota Frame. I should note here that if you are running fenders, the exposed frame would be under the fenders. From memory, I believe the Dakota frame, at the cowl location is 34" outside measurement. I do not have a 2 wheel drive frame here to measure.

I'm posting 2 pictures of my 39 Dodge pickup that is on a Dakota frame. In the side view, the cowl appears to sit completely under the frame, but I did add a piece of sheet metal to the lower cab at that point, so it may well just be a single piece of sheet metal covering the frame under the cowl. The 2nd pic is more of a motor shot, but it does show the front spring pockets outside of the hood line. Please notice that this Dakota frame is cut off at the front of the spring pockets and tubing has been added to mount the radiator support and front bumper.

Also, that motor is a 360/5.9 Magnum with factory exhaust manifolds (and EFI), and the grill shell had to be modified so the radiator fit completely inside of the radiator.