I've had a ringing sound (or squeal as some others have said) at one particular narrow RPM range on my kicker.
Yesterday, in the driveway, while working around the back of the boat, I noticed the kicker prop will ring like a bell if I whack it with a fingernail. The ringing sounds like the same frequency as the squeal when it's running; at least from memory it seems that way. The main prop just makes a dull thud. I also noticed the kicker prop was rattly loose on the shaft (just a tiny amount), so I tightened it a little. It still rings with the fingernail trick, but it's mounted differently, so maybe things will change.
I've also noticed at times a very faint version of the same sound when running the main engine. I'm now guessing that the kicker blade ringing can be slightly set off by what little vibration comes through the transom from the main when I get to just the right RPM for it.
The main prop is rubber mounted I believe (VTEC 90) and the kicker prop is just metal to metal on a spline (9.9 Hi Thrust). They're both the stock Honda props that came with the engines.
I could try a rubber bushing of some sort, but I have a feeling the blades will still ring. I need to start searching for a different prop to try as a test. Plastic, wood, rubber, whatever
Jeff