This is actually the electric door bell in my home, but it's loud and has an alarm type sound to it. The sound was recorded using a tascam dr-05 version 2 with the mic placed on the floor while the bell was just below ceiling height in my hall.
Doorbell: digital door bell, chime, ringing. Synthesised electric sound; augmented third(b-g), wireless home door bell. Recorded with zoom h4n. 24 bit, 48khz. Converted to flac.
Old mechanical door bell, not in best condition. Rattles while the switch is closed (whether it's designed to do that i don't know) and clicks rather loudly on the low bell. Not much decay.
The most uniqe door-bell i ever found. Made of 3 differet bells. The sound captures opening and closing the gate door which triggers 3 different bells. Probably it won't fit for your purpose but if so let me know in comment section:).