From Shelley,
In my experience, cuttings root most easily when they
are short (1 1/2" or so) and from new growth. I have not tried
this with honesuckle, though.
I have rooted honeysuckle by trailing the vine on the
ground. It rooted in several spots. I bet putting some dirt on
the vine every six inches or so would have speeded up the process.
I've rooted clematis that way.
You can always try woody and green cuttings and find out
for yourself what works best. Curiosity killed the cat, but satisfaction
brought it back. If I would just stop wondering how things would work
if I tried something a bit differently, I would have a lot less gardening work.