Kyle,
I use a MIMOlite to both monitor and control my doorbell. Keep in mind you will need to make a device type for whatever dry contact relay you want that closes and then opens the relay after a set amount of time. Doorbells and door buzzers are not meant to be held open inevitably, and I’ve found that building this momentary state into the device type is the most reliable way. SmartApps that simulate momentary functions are not reliable enough.