I think the problems are as follows :
When younger and child free there is obviously a large pool of potential partners, giving a decent chance of meeting one who is a 'nice' man / woman.
As you get older the nice ones will have become involved in relationships, married and very likely had a family so they are then out of the running.
Leaving all the dysfunctional ones with a few nice ones who have slipped through the net, and some who've been burned in some way and become more sceptical / guarded.
And all the while these 'nice' ones have grown older and become more set in their ways. Perhaps more cynical.
So naturally the balance between 'nice' ones and not-nice ones is unbalanced. And then you'd need to know where the few nice ones are likely to be hiding, and also whether they'd consider you equally nice or whether they'd actually want a relationship. And of course you'd likely want to find one who'd nice and fanciable and of course solvent.
And of course if they knew you were looking for a 'knight in shinning armour' they'd likely run a mile.
There are dating sites for single parents, or so I've heard, and I'd imagine there's a better chance of finding a compatible 'nice' man there. Outside of there I think there are social activities that are likely to be attractive to nice men. for instance I can't image too many non-nice man volunteering with the Woodland Trust.
The one thing that's 100% certain is that if you don't get out there, where ever there is, you won't meet any nice men.
And lastly, you know there are men on this forum, both single dads, married dads, and NRPs, we're all trying to do our best, and hearing 'nice men that's an oxymoron isn't it' is incredibly insulting.