5thcorps... Virtually any basic audio amplifier will work. The signal coming out of your doorbell is probably so low that it will satisfy line level input requirements, possibly with the voltage limited via a POT as it's intended to feed a speaker. Feed back is not a concern. I wouldn't even worry about a schematic just use an off the shelf audio amplifier.
In all honesty the proper sollution is to simply buy a better unit! The wired doorbell in my place can be heard anywhere in the house, and it's 20+ years old. Audioguru's unit is either defective, wired improperly, or he has a larger house than is typical for the unit.
Wireless doorbells are over rated, simply wiring one will save you years of hassles with batteries or reception glitches. Basic knowledge of home construction makes wiring things like this nothing more than a few hours worth of effort.