We've bought a tankless water heater & the instruction manual states only use solid core pvc, but we can only find cell core pvc. Any reason not to use it?

I have no real plumbing expertise but I have used pvc pipe. Are you sure it didn't require solid wall vs cellular wall?
Here is a link where a plumber discusses his experience and he regrets using a foam type pvc and I am not certain if that is realted to celluar or not to be honest.. Have you discussed with any good plumbing supply warehouses? Evidently the tank designer thought there was a good reason to use what he/she specified.
This may or may not shed some light on it? Foam Core PVC disaster - Plumbing Zone - Professional Plumbers Forum (http://www.plumbingzone.com/f22/foam-core-pvc-disaster-11853/)

You are talking about pvc for the venting, correct? If so, cell core won't hold up to the heat of the exhaust like solid pvc will, and may warp (basically melt). DO NOt use cell core, as mandated by the manufacturer. There has got to be someplace to get regular sch40 pvc in your area, right? If not, take a drive to get it, or order it. Don't take a chance here. Good luck, and please let us know how things work out.

PS. What make of tankless are you using. Take care.