the picture of the leaf is too dark for me to see anything but a shillouette of the leaf...but it doesn't look like a dried out leaf (there's usually some curling or cupping associated with dessication)

what percentage of the leaves are browning? are they at the tips, or closer to the crown? are there clusters of them, or are they scatterd? what is the texture of them like?

I can see the pic- the apex half of the leaf is brown. There is a clean demarkation between the green and brown. The green base shows no mottling or yellowing.

Lace bugs love cotoneaster, at least they like mine. However, the leaves usually look mottled, not half brown. If you have lace bugs, you can tell by looking on the back of the leaf. There will be brown and black specks, even if the bug has left. Cotoneaster is also very drought tolerant. Perhaps a fungus? I would ask a local nursery, they should be able to tell you.

Cotoneasters also are not overly fond of fertilizers - have you added some there recently?