Provided that the flap speed schedule is observed, there is no problem with extending flaps in descending flight. Any other method of operation is inefficient and impractical and will lead to noise violations at any airport that requires a continuous descent approach.
The descent rate will decrease as the flaps are extended, however so will the ground speed and that takes you back to the basics of flying an approach. In brief: be in full control of the speed and energy of the aircraft and tackle it earlier rather than later.
There is nothing in the FCTM to state that flaps should not be extended during the descent. The point is simply that all pre-approach manoeuvring should be completed in a clean configuration to minimise fuel burn. On a 737 of any flavour the minimum clean speed is comfortable for any initial approach segment. Flaps should not be used as speed brakes, simply because they are not designed for that purpose and are ineffective, additionally there is a perfectly good speedbrake that at any speed remains more effective than flap and the gear is always going to create drag and therefore falls under the "approved" speedbrake label.
ATC when requesting a decrease in speed require a discernible decrease. Every ATCO is different and the speed decrease is not laid down. However, 1Kt per second seems to do the job and this can be achieved in the descent without resorting to extending the flaps!