The Bougainvillea in my garden may have a few dormant periods during the year, depending on how dry it is, but it is usually blooming.
Other blooming plants are:Lemon Verbena (Aloysia citrodora,) native to South America,
Thunbergia alata, native to Eastern Africa,
and the Canna Lily, native to South America.
It is not a lily,
but in the ginger family.
This one is called the Picasso Canna Lily.