I have got a photograph on my facebook which is only visible to me, can I share on another persons timeline so that only they can see it or would it be visible to all that persons friends
I don't think you can share it so only they can see it.
Once you share a photo, you have no real control over what they do with it. If it is something you really, really don't want spread over the internet, keep it to yourself.
If there's a photo that you want someone else to see (and no one else), you can inbox them. In there, there's the option to "add files" or, "add photo".
That way, the photo goes to their inbox, for only them to see ...... as long as they don't share it on their wall, etc.