Andrew R Stewart 

The first thing I do for chirping posts is to record the seat position (fore/aft, angle, height) and then take the seat clamping assembly apart. Clean each part well, fine steel wool cuts through baked on grime. Then reassemble with a thin film of grease on each part including the seat rails where they are in the post's clamp. Many noises are just dry or loose clamps. Next up is the seat tube/post/binder clamp area. Do the same take apart and reassembly. A long screwdriver with a solvented rag does a good job in the frame. carbon parts get friction paste instead of grease. This is the next most common area to creak.

But there are other possibilities. The seat rails as they attach to the seat body can be a source. The seat tube might have a sleeve, not always meant to be removeable, that is now chirping. (Cannondale had this problem in the 1990s. they suggested soaking the frame upside down in a vat of linseed oil). I've also had seat posts creak between the shaft and the pressed in top piece which has the rails clamp.

The Op says he replaced the post so post clamp source is doubtful. Andy.