I think I now have correct the list correct of books by Rosemary Sutcliff that feature the signet ring with a dolphin design. Her signature also featured a dolphin. In chronological order the books are (click on the titles to find posts on this blog about each book; click here to find summaries of each one):

The Eagle of the Ninth (1954) – 129 AD
The Silver Branch (1957) – 284 AD
Frontier Wolf (1980) – 343 AD
The Lantern Bearers (1959) – 410+ AD
Sword At Sunset (1963) – 5th century
Dawn Wind (1961) – mid-late 6th century
Sword Song (1991) – early 10th century
The Shield Ring (1956) – 11th century

• An article by Eric Eller  at The Green Man Review about the  novels connected by the ring, and the same Acquila family