I changed my air ride system to shocks and springs on my 1993 lincoln mark 8 now my air ride system wont stop beeping

I replaced mine with traditional spring and shock suspension from Arnott. Not as cushy as air bags, but totally driveable.
https://www.arnottindustries.com/part_LINCOLN_yid2_pid7.html

AIR COMPRESSOR TO AIR RIDE IS POWERED DOWN.

There should be a level switch in the rear of the car.The connector may have come unplugged,or filled with water.or maybe the switcch is bad.Or,it could be as simple as a disonnected or broken link arm at the switch.

This is a common problem for all Lincolns. Since the front rises but can't hold the air, it's a good sign that you don't have any compressor problems. You probably hear the compressor constantly clicking on to try to keep the front end inflated.
The most common cause is a leak in the air spring. It is often referred to an "air bag" which is basically a cartridge that fills and releases air based on the load. The most common repair is to replace the air spring (it's advisable to replace 2 at a time). There is another solution to replace the air spring(s) with a conventional aftermarket shock type spring setup. It's a matter of personal preference. You would still get a nice ride from a conventional shock absorber setup. Although more expensive, I've always preferred to go with the air spring replacement to keep the classic "Lincoln" ride intact.

NOPE LEAVE IT AUTOMATIC CONTROL.LET THE HEIGHT SENSOR CONTROL THE AIR COMPRESSOR TO AIR SPRINGS.IF YOU OVER RIDE THE SYSTEM YOU COULD PUT TOO MUCH AIR IN AIR SPRINGS AND DAMAGE THEM.

the switch to turn off the air ride system is located in the trunk. It is marked

Don't bother. Check with srtutmasters or other alternatives. If the car was made in 93, all bags will be leaking and eventually the compressor cant keep up and fails. even your local lincoln dealer will not be able to diagnose the problems with their "computers." You can get lifetime struts and spring, in your case just springs for the rear, lincoln shocks still work. Put new struts and springs in the front. The only difference is the car will not lower itself at 60 mph or higher. the ride is the same.

Save your self the hassle and expence of troubleshooting and replacement parts, install a suspension retrofit kit which changes the rear bags to coil springs and the front to struts. A car this old you might as well start over for less than $500.00......

could be a bad shock or leak in the line or bad relay a few things could be wrong , I would take and have checked on a shop computer

Air Suspension Compressor Motor/Vent Solenoid : Lower RH front corner of engine compartment C134
Air Suspension Switch : Rear side of trunk C458
Air Suspension/EVO Steering Module : Behind RH cowl panel, above connector bracket C204, C205
Air Suspension/EVO Test Connector : RH side of engine compartment, top of wheel well C117 Soft Ride Relay : Under center front of package tray C403Hard Ride Relay : Under center rear of package tray C404 sorry could not find compressor rely listed, good luck