I have it, reasonably recently diagnosed, but I am getting treatment (counselling) on NHS and privately.
Does he permanently refuse to seek treatment, or just during certain points - e.g. peaks of depression or hypomania?
There's an excellent book - 'The Cyclothymia Workbook' by Prentiss Price. It's got explanations, symptoms, solutions, worksheets etc., and is aimed at both the sufferer and their family. I'd recommend buying it.
CBT is a pretty fundamental part of dealing with it, but it does require work.
I know it greatly upsets my OH sometimes: when I'm down I can shrink into myself and be uncommunicative and generally crap to live with. On the other hand, during a hypomanic phase I am great fun but can also be frustrating because I'll overdo things. My aim with the therapy is to reduce the peaks and troughs, although I doubt I'll ever get rid of them completely. That said, I'm not entirely sure it's something I'd want to eliminate completely from my life: the positives of creativity and a love for life it can bring are great. But managing the downs is huge for me, as I can just opt-out of day-to-day life, which causes problems.
The big concern for you should be his refusal to seek treatment. Why? Does he think it makes him weak? Does he deny he has a problem?
My ex had depression (before I was diagnosed) and so I have experienced both sides - living with a partner and having a problem myself. Personally, I could live with someone who was making genuine efforts to help themselves, but an absolute refusal to admit there's a problem and seek help would be a deal-breaker for me, and to be honest, if I didn't want help now I wouldn't expect my new, wonderfully-supportive partner to stay with me.
I've also (very recently) cut out alcohol, as a) I think there is a bit of a link between drinking and my down periods; b) I was using it to self-medicate and push away problems and c) when I'm in a hypomanic cycle I completely overdo it.
Depending on where you are in the country, there will be a variety of support from the NHS, but your GP is the place to start. I got referred to a group CBT course (not therapy, but learning how to implement CBT into your life). It was hugely useful, although I've fallen back on implementing it properly, and I'm about to start a 1-on-1 telephone counselling course. If that doesn't work I'll be 'upgraded' to in-person counselling on the NHS.
There are also online counselling services, e.g. Betterhelp, where you effectively email a counsellor - the same one, so you build-up a relationship - which for some is easier than having to talk in person. The downside is that it costs about £150 a month - although that's cheaper than 'normal' in-person counselling would be.
If it's untreated, it can develop into full bipolar.
To be blunt - and repeat a point I've already made - the first step absolutely has to be his admission there's a problem. You simply cannot help someone who won't help themselves, and you may find, as difficult as it will be, that you have to give an ultimatum, and be prepared to follow through with it. One thing's for sure, if he refuses to get help, the rest of your life is going to be pretty crap.
How much have you talked to him about this? Does he give reasons for not wanting help?
Here's some reading / watching material:
Cyclothymia:
ashleybraeden.blogspot.co.uk/p/cyclothymia.html?m=1
CBT self-help:
www.getselfhelp.co.ukstep1.htm
Person-centered therapy:
en.wikipedia.org/wiki/Person-centered_therapy
Bipolar Disorder Research Network
bdrn.org/
Stephen Fry documentary - he did have cyclothymia, but it was either initally misdiagnosed or developed into bipolar:
Feel free to private message me if there's anything you want to ask that you don't want to post in public.