Wow... it's been almost 2 weeks and no-one's replied!
Hope you're still watching the thread, dude.
First question though... what sort of system are they using?
Don't be afraid to ask them.
It might be that they have someone who looks after transferring audio into the phone system for them, so it may be as simple as you supplying a CD or wav file or something like that.
If it turns out that they just have to record through the handpiece, I have achieved perfectly acceptable results by playing the recorded message
at speaking volume (that bit is critical) from a boombox in a quiet room (ie no extraneous noise) into the handpiece from the same distance as you'd normally speak. In other words, put the speaker 2 inches from the mouthpiece of the phone and play the message at a normal "spoken voice" volume. You might be pleasantly surprised with the result.
Just don't
act surprised in front of the client, ok?
Tell 'em that's how the pro's do it.