Word to describe someone who rarely gets upset

Solution 1:

Unflappable describes someone who remains composed in the face of adversity or scandal, "impossible to fluster."

Stoic has the same meaning, but often implies indifference to pleasure as well as adversity.

Solution 2:

The state you describe is equanimity:

noun [mass noun]
calmness and composure, especially in a difficult situation:
    she accepted both the good and the bad with equanimity

[ODO]

The adjective is equanimous.

adjective
calm and composed.

[ODO]

However it would not be the best choice in normal use. Google Ngram

Solution 3:

How about placid? From Merriam-Webster.com: Definition of PLACID:

serenely free of interruption or disturbance

Solution 4:

Easygoing.

Seán is really easygoing and it would take a lot to phase him.

Solution 5:

Phlegmatic is another word that fits, although it fits 'stoic' better than 'happy':

From Google search definition: phlegmatic — (of a person) having an unemotional and stolidly calm disposition.