I think the following couples are happy (or at least I hope they are):
Victoria and Daniel
Willem-Alexander and Maxima
Richard and Birgitte Gloucester
George and Sophie Hohenzollern
Harald and Sonja
Elizabeth and Philip
Felipe and Letizia
Marriages of convenience, or long-term marriages in which they are at least content:
Philippe and Mathilde
Albert and Charlene
Margrethe and Henrik
Benedikte and Richard SWB
Albert and Paola
Michael and Marie-Christine
The following couples don't exactly exude happiness:
Fred and Mary
Joachim and MarieEdward and Sophie
(I just get a whole miserable vibe off Sophie lately)
CG and Silvia
JC and Sophia
Martha Louise and Ari BehnEdward and Katherine Kent
Cristina and Inaki
Henri and Maria TeresaCharles and Camilla (I think they used to be, but not anymore)
I can't decide where to put Haakon and Mette-Marit. Sometimes they look happy, sometimes not. As I said above, I hope they are
With regards to Edward and Sophie - they aren't a PDA couple, they never have been. We have only ever seen one image of them kiss in public. It's just not their style, but I don't doubt there's love there. They rarely hold hands in public. You can see some of the glances between them that are just lovely. They have been together for 20 years this year (married for 14 this year) so perhaps "the spark has gone" but they still care about each other. I can't imagine they would ever divorce, unless something major happened. I think their marriage is for keeps.
Edward and Katharine Kent - Katharine chose to lose her HRH style and retire from public life after a history of depression (after birth of a stillborn son Patrick) and illness (suffers from Chronic Fatigue Syndrome) with permission from The Queen. It is said they live separate lives but never divorced as it was nixed by the Queen after all the divorces in the Windsor family at the time.
Charles and Camilla - I see the love between these two all the time, more than any other couple in the British family (aside from the younger generation).
The British Royal family are not a PDA family. The British in general are a stuffy population, so we will likely never seen the couples be affectionate in public.