As others have mentioned, for savory pastries, there are various types of crusts that are meant to be held in the hand, and are thus not likely to be either flaky or crumbly. Examples are pasties, calzones, or even pizza.
For sweet pastries, you could look into the sort of pastry used for, e.g. Hungarian-style apple pie (almás lepény).
Granted, this isn't what most English-speakers think of when they hear "pie", but there's no reason you can't, uh, "borrow" some ideas from it.
The pastry is made with the usual flour, baking powder, butter, and sugar, but also eggs (either whole or just the yolks) and sour cream, and the whole thing is lightly kneaded together - there's no cutting the butter into the flour1, so you're not likely to end up with anything flaky. And since sour cream makes everything better2, the pastry will be moist and tender, not dry and crumbly. Here's one English-language recipe and instructions, and there are many others out there. (Though if you find one that calls for milk instead of sour cream, run far, far away.)
1 Well, OK, so some recipes do overcomplicate matters, using cold butter and a pastry blender and whatnot, but it's really not necessary.
2 Really, it does. I know this honor is usually accorded to bacon, but I ask you, would bacon really improve a nice sour cherry pie? I thought not. Whereas sour cream can really do anything - use it in place of whipped cream in a pinch, slather it over your chicken paprikás, use it in both sweet and savory pastry doughs... but I digress.