Agreed that a stock screener is the way to go for this. Some let you customize your criteria more than others. http://www.stockrover.com has a Dividend Screen as one of the defaults with the values that screens companies that have:
A market cap of $1B+
A Dividend yield >3% and <10%
A Dividend percent change during the last year >2
A Dividend percent change during the last 3 years >2
A Dividend percent change during the last 5 years >2
A payout ratio >30 and <60 (Dividend Per Share as a percent of Diluted Earnings Per Share)
Clicking on that screen TODAY shows returns 52 stocks, but to refine further you can simply change the variables and see the number of stocks that will pass the filter change in real-time, and you can save the edited screen so implementing it is as easy as clicking on it next time you log in.