Do you live in Cyprus or Malta, or are you wealthy (able to easily deposit 100-250,000 EUR be comfortable leaving it there)? If not, chances of success are extremely low.
If you are resident in Malta or wealthy, the most popular local banks are BOV and HSBC. Both are pretty terrible to deal with. It's a cointoss.
If you are resident in Cyprus or wealthy, you have more options and more variety. Bank of Cyprus, Hellenic Bank, Alpha Bank, Astrobank, and RCB have their pros/cons.