All Serbian banks which I wrote said that it's impossible. Maybe you can do this using POA. Actually, some banks in Georgia provide such possibility to use POA.
CIM Banq, Ameria (Armenia) - with mandatory Skype call.
N 26, Paysera - you will need a postal address at EU or friend, which can send you the card. Transfers only in SEPA.
Different offshore banks, but there is min. deposit started from 5k USD mostly. Banks like BOSLIL, Hermes Bank etc. And in the most,︀ they don't provide cards.