You don't need to contact anyone locally for some banks. You just need to email them, send your documents and other requirements, pay the fees and you're done. As long as you submit the right documents you can easily open it without anyone visiting the bank.I don't think you will need to visit Cyprus to open and bank account. You can contact any locally by living in Cyprus and save them to manage your account on your behalf.
You need to try and find a good bank of your choice and send them an e-mail regarding your question. Since it depends on the bank if they wanted you to visit or not.I can open the account from where Iam by e-mail only, will I need to send any documents to you by mail?