How do you say Happy Anniversary in Swahili?

There are no real Words for anniversary and birthday in Swahili. The following two options could work:

Furaha ya sikukuu yenu = joy on your (pl.) special day

Heri ya sikukuu yenu = blessings on your special day

In practice though, many Swahili speakers use the English Word "anniversary":

Heri ya anniversary

Furthermore, birthday can be expressed as siku ya kuzaliwa (day of birth), but most people use the Engish. Heri ya birthday, blessings on your birthday, equivalent to English happy birthday.