Perhaps a ring tone that is really low.
Perhaps not. OBi ATAs do not have fully programmable ring tones. The only controllable parameter which is available for distinctive ringing is the cadence - the pattern of ringing and no ringing. Connected to a phone that is not mains-powered you might be able to adjust the volume of the bell or beeper sound by changing the ringing voltage sent by the OBi. However that is a global parameter which affects all ring patterns so you cannot have calls on one SP ringing more quietly than other SPs. If the phone is mains powered, reducing the ringing voltage may have no effect except to stop ringing at some threshold point.