This Great Graphic comes from Charles Schwab's Liz Ann Sonders, and was posted on Business Insider. It identifies periods of US Dollar Index strength and weakness and looks at how the S&P 500 performs.
One could pick at the periodizations she finds. One could pick at the measure of the dollar, which is the Dollar Index, and heavily weighted toward Europe. Yet for an exercise, this is a quick approach.
As it turns out, the S&P 500 has generally advanced regardless of whether the dollar is in a bull or bear market. Bull markets for the Dollar Index have seen a larger rise in the S&P 500 than a dollar bear market (almost 59% vs 31.5% on average). Averages may be misleading. The 10-year Dollar Index rally ( 1991-2001) that Sonders identifies saw the stock market gain nearly 231%. The 1978-early 1985 dollar rally also saw an outsized 88.5% rally in the S&P 500. Besides these two, there was only one other bull market for the dollar that saw the S&P rise more than its "average". Moreover, two of the five dollar bull markets coincided with weaker stock prices. No bear market for the dollar saw US S&P 500 sell-off.