I want to say “a son was born for the king and queen”
or “a son was born to the king and queen”
Which one should I use?
The idiom is “born to” (though it is a bit literary, as is using the passive at all in a case like this).
“Born for” does not exist as an idiom, so using it would imply that in some unspecified manner the son’s being born was to the King and Queen’s benefit – it would not even necessarily mean that he was their son.