It actually depends on the type of media converter you have. See if you can use a passive media converter rather than an active one. Also, see if suppressing Keep-Alives (no keepalive) on the router helps.
A media converter HAS to be active, it is converting from copper (RJ45) to Fibre, so it must do some processing, otherwise it is not a media converter, just an adaptor.
Much more likely is that you need to set the speed and duplex on the Cisco switch port. It is also probably worth adding the ‘portfast’ command, so this goes into a forwarding mode immediately. Just check the network topology to make sure there is no risk of loops. The media converters don’t have many settings, so look to fix this from the Cisco switch side. – Blank_Reg