I am not entirely sure if governments will have their own (wish they do) but I am 100% sure that banks will have their own coin.
Even if not for anything related to customers they may end up doing it as a test, sure that won't be official and be used but they know they need to check out blockchain and how it works so they will make a new blockchain currency for themselves and they will definitely want to implement the best parts of blockchains into a currency, that would have been something awesome but we still don't know if they are doing it or not. Sure they must be working hard on figuring it out but not sure if they have implemented any parts of it.
Some banks are working with Ripple for some huge movements we know that but that's about it. Banks need to adapt because if some banks implement it they will make it cheaper and faster so they will get ahead of the competition and all others HAVE TO work on it to catch up so it is going to get common eventually.
If we talk of banks having their own coin, i think that it would even be stupidity or lack of knowledge for government to see that this happen, because in every country, we have hundreds of banks, if government does not create a particular cryptocurrency which will be used by banks generally, the market will be very saturated with banks coins since very bank will be creating their own coin separately and how many customers do they really have for them to have the value of the coin increased?
I would see this as duplication system because it would involve people have the coin for different bank, and that coin, what exactly would it be used for? To be able to buy things In other sites? So how many coins does an ecommerce site want to accept before they are known to accept cryptocurrency, this I dont think banks would want to create their own currency.