I have a 56 with a perfectly good Ford o matic... The problem is the the converter stalls at such a low rpm that it is difficult to get it to idle in gear. My question is, will a non air cooled converter fit on the input shaft and pump on the 56 transmission

RB  The 55/56 FOM torque converter can be replaced by a 57 FOM liquid cooled T/Q as the input spline counts are the same. The number of splines on the input shaft AND the starter ring gear changed in 1958 when the FOM was renamed the COM.
I was given a quote to re-stall the T/Q in a 1955 FOM air-cooled T/Q some years ago. Have you tried to get your T/Q rebuilt and a higher stall added? Pete

I have not tried that... I figured no shop would touch it..  You have any names to try.. I might try Broader performance.. He is a good guy

The Converter for Air Cooled has Fins designed to draw Air through the Vents on the side of Bell Housing. The Liquid cooled Ones do not.  

  

It sounds to me that you have a small vacuum leak at the engine, your car should idle at about 600 RPM in gear, it should not stall.

The original Idle Specs for Automatics was 475 RPM in "Drive".

  

There is a slightly warmer cam in it.. Factory idle rpm specs do not apply.. Cam pulls 16 inches of vacuum, but it takes about 850 rpm idle to prevent stalling when you drop it in gear. In my way of thinking it needs a looser converter

Remember, as the stall speed is increased the temperature of the trans fluid will be raised so if cooling can`t be increased then as A/T fluid rises above 220/230 degrees F the fluid will break down sooner and must be replaced more often. Pete

Royce:
The problem with using a later converter is the starter ring gear.  On pre-58 Fordos the ring gear is on the converter front half.  Later COM converters will fit the front pump and input splines (provided your present one is 29 spline, not 17), but will have no ring gear.  You will need a '58 or later flex plate, which are getting difficult to find.  A converter rebuilder should like working on yours, they don't even have to cut it open, just take out the bolts.  They may not be able to help the stall speed much, because most stall converters are smaller diameter than the original.  Pegleg has worked with a rebuilder in his area that fixed him up with good FMX/Y-Block mongrel.
John

John - "The Hoosier Hurricane"

John that is exactly the type of info I was fishing for.. I have one of the later flex plates.. All I need is about another 500 rpm of stall speed to make the car a little more friendly to drive in traffic..