Check for aphids. They totally destroyed mine last year.
Joann

My honeysuckle buds are always crawling with aphids but they don't eat the buds. They just suck the juice out of the plant tissue and the honeydew they secrete can cause problems like mold to develop. I buy thousands of ladybugs and release them on the affected plants at dusk. That way they have a tendancy to stick around and eat the aphids instead of flying away. A single ladybug can consume a whole lot of aphids and they'll lay eggs. The larval ladybugs eat even more then the adults.

ditto aphids. Get a hose and spray them off the plant to start. Their juices, which you won't see at first, leave black spots later. Crush as many as you can, as often as you can with your fingers. You can plant marigolds at the base but it's better preventative than cure and even then, highly imperfect. If you have the time and it's under 80 degrees for the next week, you can spray the aphids with neem oil+water+castille soap daily until they disappear, but it's hard to cover them if they are inside the bud. It only works if you cover them. If you get lady bugs, make sure they come with their own food, so they will stick around. I know there are people who have honeysuckles without aphids, but I've never met them. If it's a problem, consider adding new type of vine and letting it take over while you phase out honeysuckle.