My longest relationship is with my parents and this one spans over forty years now, LOL. Well, you did not specify what kind of relationship :)
It is not the happiest, but this one has only one option, we don't choose our parents, we live to learn.
Relationship with friends are quite different, but I would not measure them by happiness. More by duration and the depth of the connection.
As far as romantic relationships go, I was married for 16 years and it is a record from the wedding day to the day of the marriage dissolution. But I met my ex in 1987, when I was 16 and regardless that the piece of paper says that we are divorced, we are connected forever if for nothing else but for our son. That makes it 24 years and counting. Nobody will be like my ex to me and no relationship can be compared to my first marriage. It will be something completely different. A different bond.
Was the relationship the happiest? There is nothing else to compare such relationship with. Even if I may or may not be in love, love is not marriage. My dating nowadays does not qualify for such comparisons.
I don't even know how to evaluate relationships on a happiness scale.
Happiness is more of a feeling of euphoria that is more characteristic for infatuation and infatuation is always a beginning of love. Then other things happen.
I don't even think other people can make me happy. It is wrong to expect them to do such a thing.
A happy relationship with anyone for me would be the one where I am understood and the one where I can laugh a lot.
Not too much to ask for?