Chrysler used the C171 compressor as standard issue with factory air conditioning systems in 1987. To remove the AC clutch (which can be done with the system charged with refrigerant) you have to remove a 13 mm nut on the compressor shaft and then use snap ring pliers to remove an internal snap ring. There are threads on the inside surface of the exterior clutch plate that mate with a special puller and allow the clutch plate to be removed. You could check an auto parts store and its loaner tools and maybe find the special puller. Don't attempt to use a hammer or screw drivers as a pry removing tool. Once the exterior clutch plate is removed there is another snap ring that holds the clutch electromagnetic coil to the AC compressor body.
You probably have either the 2.2 liter or 2.5 liter 4 cylinder engine as the power plant in your New Yorker. Starting in 1991 Chrysler phased in the usage of a Denso compressor in anticipation of the switch from R12 refrigerant to R134a refrigerant. I would suggest upgrading the compressor to the Denso type. You need to locate a 1991 - 1995 Acclaim, Spirit, Sundance, or Shadow with AC and the 2.5 liter 4 cylinder to find the correct parts. 1991 was the transition year so you need to make sure the donor vehicle is using the Denso compressor and not the C171.
To use the Denso compressor you will need the engine mounting bracket, belt pulley idler bracket, belt pulley idler, and drive belt. On 4 cylinder engines the AC drive belt for the Denso compressor was 1 inch shorter in overall length than the drive belt used with 4 cylinder engines on the C171 compressor.
You will also need the suction and discharge hoses from the Denso compressor as the mounting boss for each hose to the compressor suction and discharge ports are different from the C171 compressor. The suction hose mounting at the expansion valve and the discharge hose mounting at the condenser are the same between the 2 different compressors.
Also keep in mind that through the 1993 model year the Denso compressor had the suction port on the compressor manifold head. Starting with 1994 models the suction port was moved to the suction line. You have to watch this or you can end up with a configuration of year mis-matched hoses and Denso compressor with no suction port and capability of charging refrigerant into the system.
These were the issues I encountered in changing a C171 compressor on a 1989 Plymouth Acclaim to a Denso compressor retrieved from a 1993 Acclaim. Retrofitting a later model compressor is doable but not quite as simple as one would think.
