That suggests they are quite young pigeons (they only live for 2 -3 years actually.) I think you may require more than one cd, have you a compilation box of something you hate lurking in the back of a cupboard? String them up - cd's not birds........although........No we are being humane.
I think you should also consider something that makes a bit of a noise - small bells, babies rattle, laughing gnome.
Otherwise I'd suggest netting, you can get cheap 'pond netting' at B&Q type places which should do the job. Make sure it's fine so as not block your view but also has small holes so they can't get caught in it.