Okay, here's the Showa Timeline explanation:
Godzilla (1954) - 1st Godzilla dies
Godzilla Raids Again - 2nd Godzilla emerges
King Kong vs. Godzilla
Mothra vs. Godzilla
Ghidrah the Three Headed Monster
Monster Zero
Godzilla vs. the Sea Monster
Son of Godzilla
Godzilla vs. Hedorah
Godzilla vs. Gigan
Godzilla vs. Megalon
Godzilla vs. Mechagodzilla
Terror of Mechagodzilla
Destroy All Monsters
There ya go.
There are several other "monster islands" we see before DAM.. we see one get destroyed at the beginning of Godzilla vs. Megalon, there is also more than one Mothra, Angilas, and Rodan.
Enjoy!
EDIT: As musukogoji said above, Monster Zero could take place in 1965-1969.. whatever fits your fancy.
I personally keep it before the "island" movies, since those years in between Monster Zero and Hedorah I think Godzilla is trying to "rest".