There are almost any of the banks in Cyprus that may work for your business. They have all some great Internet banking and multi currency accounts. Most often Piraeus Bank and Bank of Cyprus are the banks the client choose.
I see Piraeus bank Cyprus mentioned many times when it comes to offshore banking... what other countries / offshore jurisdictions are there with great banks for easy account opening?
Hellenic and Piraeus are the best banks to bank with in Cyprusm however, it seems it's been more complicated to apply with Piraeus compared to other banks and the past.