Appearing visible to selected contacts in Skype

It's been requested for years on the Skype community forums, or just outright shot down, but currently, this is not possible to do.

Your current options include:

Creating an entirely new account and only adding in the contacts from your original that you wish to contact you whenever.
Set yourself as "Do Not Disturb" and hope those you don't want to talk to won't talk to you while you're set at that status.

Or just stay invisible and continue messaging with a select few contacts only.

I don't know of any selective status display, but as an invisible user you can still receive calls. Your caller just won't know beforehand whether you're "on" or not. When they attempt a call it will either ring or report "User is not online".
You could either let those few people know when you've signed on via Skype IM, or tell them you're staying invisible and to try anyway. (Obviously this only works if you're willing to have that select group attempt to call anytime; if you're going to change by whom/when you want to be called when invisible, you'd need a true whitelist.)

Block them temporary, by right clicking on the user > click Block this person. you'll see as invisible and don't get messages.When you unblock, you can get messages all messages above(with block time messages)

For Windows Skype: