If I'm reading the Danish fare schedule correctly, the metropolitan fares including train from CPH is:
CPH to central station = 36 dkk
Local bus in zone = 24 dkk.
Ticket machines take coins. If memory serves me, 20 dkk, 10 dkk work in the ticket machines and return change. We paid the bus drivers in coins and got change back.
Our credit card (Cap One) is a chip and signature accepted at staffed pay stations but we didn't try it in a machine. Denmark is pretty advanced and seemed to accept credit cards everywhere. If you use the airport ATM cash machine as I did, it returned only 500 dkk bills (I asked for 1500 dkk). I used one of the 500 dkk at the airport's staffed train ticket office.