I have contemplating about this and even consider capturing data however havent had a chance yet.
I presume if the coin price plummets then people will lose interest and move to other profitable coin and as a result, falling coin's difficulty would decrease but so far I havent quite noticed that with zcash. Sometimes it seems opposite is happening.
But I'd really need to capture long term data over long enough time range to see any relationship and/or pattern being observed.
There is no simple consistent relationship between the two.
Mining difficulty alone isn't sufficient for making accurate predictions of coin price, nor the other way around. Perhaps you could make general statements, such as "If all other factors are constant, and coin value decreases, then we would expect the mining difficulty to decrease as other options are explored."
If there is a time where a coin is primarily being used by miners looking to make a quick profit with a different preferred coin, they would simply dump in favor of that preferred store of value. If such were the case, then we would expect the price to drop as miners continue to sell their coins to a smaller pool of spectators.
That behavior is not typical of successful cryptocurrencies. Miners are never the only users of a such coins. A large number of people are always in it to speculate, whether that's simply because they believe the value will increase, or because they value the coin itself based on the merit of the system and its ability to be used as a medium of exchange.
Mining alone does not account for enough of the variation in coin price to make good estimates. The behavior of speculators will always influence the value and is inherently difficult to predict.