Yeah in your case, besides a good lens coating agent, I would look at some kind of "sun shield" although in this case I guess it's a "rain shield". I would imagine there are some camera accessories that would work here. I say this because although there are dedicated "sun shields" made for weapons sights, they are more expensive and probably harder to find in the right dia. So taking a page from SOT's playbook, I'd look at what's available from camera accessory guys. Ideally something in 30mm that would screw right into the obj lens, or at least something that would slip over it.
Thinking in terms of field expedients, Marine Scout/Snipers used toilet paper tubes, duct-taped to the scopes to reduce glint. The same technique would apply to rainy conditions. Finding a light, water-proof material to fabricate a field expedient "rain shade". Light gage plastic tubing comes to mind. Maybe in conjunction with a rubber tube as an interface or adapter.