I've had serious happiness issues with certain settlements on previous play-throughs but with my current one I was determined to find out what the heck the issue was.
With my current game I had issues with Ten Pines Bluff and Abernathy Farm. Abernathy has been a thorn in my side since I started playing and after some research it appeared that the issue had to do with the original settlers (the Abernathy's) and their beds. Following a suggestion I assigned them to different beds and low and behold, the happiness started going up where it had once been stuck bouncing around the low 60's.
I noticed later while doing a settlement book-keeping tour that Ten Pines was having issues with the happiness, staying in the low 60's as well. I popped over and saw that there are 3 "original" beds in the settlement: 2 mattresses in the original shack on site, one in the ruined building at the other end of the build zone. I could scrap the single one in the ruins, but not the two in the shack.
I decided to sleep until 3am. The two mattresses in the shack were occupied and the other 14 settlers in the settlement were clustered in the middle of the zone. I assigned the two sleepers to beds in the structure I built by the ruined house. By the time I ran back to the mattresses to get the second settler, the non-sleeping settlers were starting to form a line into the damn shack!
Yep, every last settler in Ten Pines wanted to sleep on those two original mattresses! Every time I'd assign one to a bed I had crafted, another settler went to sleep on an original mattress.
It gets better. I decided to move those mattresses closer to my bunkhouse in order to shorten my trip once new settlers appeared. The only way to move them is to grab them like you would something you want to move in the regular game world (in this case, targeting the mattress and pressing and holding E) while in construction mode. What really svcks is that I placed them near my structure and now when I try to move it, I also pick up any constructed items nearby! Even though it isn't touching it, if the mattress is even near a crafted item, you'll pick up that item (houses, water pumps, crops...you name it).
My advice is to scrap any original bed you can in a settlement and to move the ones you can't to an area you don't plan on placing structures, crops or the like. If your happiness stagnates, try assigning all of your settlers in a settlement manually to beds. If you roll into a settlement at night and everyone is standing around clustered up, you probably have a bed bug...pun unintended but left because it made me chuckle.