What advice can be given to non-Muslim parents whose children have accepted Islam, but they are not yet ready to do so?

“Be patient and never give up on them. Meet and always be in touch with them. Let them feel that Islam has brought you closer to them than ever before.”

I speak from my personal experience. My parents took 21 years to accept Islam after I did. When I accepted Islam, naturally I wanted everyone to accept it, but it does not work that way. After I had basically given up on my parents, they said that they wanted to accept Islam.

So the key word is 'patience'.