When I'm driving my 1991 FC coupe 5 speed, and I lift with the car in gear I hear a clanky sound which is coming from underneath the car. The sound is loudest if I lift in 1st gear and coast. The sound gets quieter the higher the gear and is basically non existent in 4th and 5th gears. This sound is not present while rolling in neutral or sitting still with the engine running or rolling in gear with the clutch engaged. Only when im driving in lower gears and lifting off the throttle while staying in gear do i hear this very annoying "clanky" sound, definitely sounds metallic.

 

Sounds like classic symptoms of a broken front differential mount. This is the mount that attaches the snout of the diff to the subframe. Search "diff mount" or "front diff mount" and you are sure to find many results.

 

Besides the diff mount,it could be something easy..like the heat shielding on the bottom of the car.
But really this requires you to lift the car up and look as it is not just isolated to one thing.

 

what about the strange occurrence of quieter noise while driving in the rain compared to driving in the dry with the noise being louder and more often than when it's wet??

 

rain is more then likely muffling the sound as it's being passed under the vehicle. I agree with styx, get that car in the air and start looking at the diff mount and heat shielding of the exaust. It could be a combination of worn out parts.

No use "dwelling" on it, do work.

 

Check the driveshaft u-joints too.

 

Noise is beginning to sound while accelerating too, quieter in the higher gears

 

We've already told you what to check and the car isn't going to magically get fixed.

I think you probably need a new driveshaft.