The resistive touchscreens that were used in the 1990s and early 2000s would suit you, since they would be insensitive to raindrops. Of course they were also less sensitive to fingers, and couldn't handle multi-touch gestures, which is why no phone uses them these days.
With capacitative touchscreens you are out of luck. They respond to contact with conductors, and larger raindrops are hard for them to distinguish from being touched by a small bag of salty water (aka a human fingertip). Some may be better than others in this regard, though it's not something that the manufacturers publicise if so, but none will be immune.
Basically keep the screen covered when not in use, try to shield from rain when using, wipe dry when you have problems. You could experiment with whether keeping it in a bag would help (so water is not directly in contact with the screen). That's all I can suggest.