I have a 1969 Mustang Coupe with a 351-2V Cleveland. Is this the original engine or did someone drop this engine in? I understand that the Clevelands were only on the 70-74 models.

Do a google search for "Mustang VIN decoder" or check a Chiltons manual for your car's VIN identification. By checking the engine code part of your VIN number, you will be able to find out what your 'Stang came with for an engine.

The clevland engine wasn't distubuted to the public until 1970. you need to find 4V Heads for that engine it'll runs better and have more horsepower. thats what i did

You are correct - 1969 351's were all reported to be Windsor’s - 351 Cleveland’s started in 1970.
351W 2V was the standard engine in the 69 Mach 1's, the 6 cylinder was standard in the others.
The 5th letter of the VIN is the code for the engine in 69, - T =200 I6, L=250 I6, F=302 2V, H=351-2V, M=351-4V, S=390-4V
If your 351 has the radiator hose thermostat housing built into the intake manifold, it is a 351W, if it is separate, it is 351C.

351 cleveland was an option. Mostly on the coupe and grande models

i also had a 69 coupe, it came with a 6 cyl. and 3 on the floor. it was yellow, i had it painted forest green, dropped a 351 cleve motor in, and proceded to lose my license. But what a blast, it would do incredible burnouts, went over 125 mph easily, ahhhhhhhh the memories, idk if they ever came stock with that motor. sorry but just wanted to tell you what a great time i had in that stang. yo bud, buster