Andy, you're trying to be spoonfed here. I assume you want something with a lot of liquidity, so what you need to do is get you a list of the Nasdaq 100 and the Dow. Then do some research. A very few are out there.
Answer: A board of directors consisting of overweight, cigar smoking, white males in their seventies and eighties. I.e., your basic utility company.
Not sure why anyone would want a "stable" stock that goes nowhere anyway....Why spend money that you could be collecting interest on to gamble on some stupid that doesn't go up? And "could" go down. A "Value" stock, yes, good P/B and P/E etc. of course. Try a broad based ETF perhaps. Don