What kind of reward will the miners have when coins are no longer mined?
All coins will be issued.
That will be quite a few years in the future ago - so I guess difficult to tell at this stage.
I would like to hear a more specific answer.
Once all coins are mined, as far as I know, it simply won't be possible to mine more. There's some mathematics voodoo involved that's way above my pay grade to ensure that.
Of course, take this all with a grain of salt.
Short answer: Tx fees.
Long Answer: Zcash is following Bitcoin's supply curve (https://en.bitcoin.it/wiki/Controlled_supply), the only difference being shorter block times with proportionally lower block rewards (ZEC: 12.5 every 2.5 minutes, BTC: 50 every 10 minutes).
It's estimated that the last BTC will be mined around the year 2140, so the last ZEC won't be mined until around the year 2147. It's assumed that by that time the tx fees of the entire network will have grown significantly, and it's believed that those transaction fees will be sufficient to incentivize miners. While this may or may not occur as planned, it largely depends on mass user adoption and an exponential increase in the number of tx per second, which brings up the whole scaling debate currently facing Bitcoin.