Doorbells are usually AC so it probably doesn't matter. But if you were having problems you may have the wrong transformer for that doorbell.

When was it "buzzing" - when the button was pushed? Why did you wire the resister in parallel and not in series?

It was buzzing when I put the breaker back on regardless of the button push. I did it in parallel since it was easier. Should it be in series? Thanks!

Sound like a problem with the button or wiring. Did it still buzz when you disconnect the button? Does the button have a light or anything? I assume that the old doorbell worked and didn't buzz.

10 ohms (and looking like a 2-watt resistor) is a very low value just to prevent buzzing.

Did you experiment with higher values and they did not prevent the buzz?

No I haven’t. Would 8 watt resistors work?

I think The Logician was saying that 10 ohms is very low - not the watts.

Yes, the ohms value seems low. the doorbell transformer would be capable of burning the resistor if the transformer voltage was applied to it for many seconds, like someone holding the doorbell button down. Unlikely, but possible. Try 100 ohms (brown-black-brown stripes), and if still buzzy, some value in-between.

Ok thank you Logician!