Well, I didn't have a relationship longer than 18 months until I was in my late 30s, and I had plenty of big gaps between relationships. In addition, the people I did have relationships with were generally pretty damaged fuckups and weirdos- because I was fucked up, with low self esteem. I had DS on my own after a short relationship with an EA man. Yet, at the age of 38 I met DP through OD (first date on OKCupid!), he's great and we've been together 2 years now. In analysing what changed, I'd say the following:
After having DS, I stopped putting so much emphasis on being in a relationship- in other words, got stronger in myself and less needy;
This led to an upsurge in self confidence- more confident in going for the people I felt to be right for me, more confident in ditching the ones who weren't;
Feeling more resilient, so that I could message blokes online and not give a shit if they didn't reply (and yes, I had quite a few not reply!)
In addition to this, I concede that I was also pretty lucky to meet a good'un on the first date after DS (I had also tried a bit pre-DS and had no luck). So, in short, I guess I'm saying it was a combination of factors- yes I was lucky, but we all get lucky breaks sometimes and I had to be in the right place mentally to recognise one.
So I suppose what I'd advise, OP, is first of all to do a bit of work on yourself- counselling, building your resilience, concentrating on being happy in your own skin. Maybe knock the looking for a man on the head completely for a year and work on enjoying being you? (I don't mention this airily; I was unhappy and felt a failure being single for years, and it was only after I had utterly ceased to give a shit that I met DP).You may find that life changes for you in many unexpected ways just from doing that.
A couple of thoughts about when you do actually date though. Many of the decent single men in your age bracket are going to have children. The ones who don't in their 40s may just be waiting for the right woman to happen along- or they may be immature man-children who will never be able to cope with fatherhood. You can learn an awful lot about how good a man will be as a potential father from his relationship with his existing kids. And, in the very long run, it could mean your future children would have ready-made siblings- not a bad thing. So, I really wouldn't rule men with kids out, at all.
The other one is a bit frivolous, but- if you're looking for a man-heavy activity, you could do worse than give sailing a go. Seriously single-man heavy if you're not picky!