Dragon and Monkey.
Three harmonies
Same team: both signs belong to one of the four groups of three. On the wheel the two signs sit 4 places apart.
The three harmonies group the twelve signs into four teams of three. Two signs on the same team want similar things from a year and move at a similar pace, so the pair tends to agree on direction.
Agreement on direction is not the same as agreement on method. The friction in a trine pair usually comes from wanting the same thing in different ways.
Beyond the year sign
We compared 200 Dragon and Monkey birthday pairs born between 1950 and 2005. The year sign changed little across those readings. Even classical clashes covered nearly the same range as harmonies.
The deeper charts varied much more. One person's nature could support, restrain, or closely resemble the other's. The year sign sets a tone. The two exact birthdays decide the pair.
What this leaves out
The year animal is one of eight characters in a Chinese chart. The day pillar says more about a person than the year, and a full reading compares all of them. The year also turns at Start of Spring, around 4 February, not 1 January, so people born in January or early February usually belong to the previous year's sign.