Does the Bitcoin Core API support high-precision balance display? I am currently working with a number of altcoins and and I need to support deposits and withdrawals in currencies with very large coin number cap like Dogecoin. I am wondering whether the Bitcoin Core client that is the basis for such altcoin clients supports such high denomination currencies internally and in its API (for example, when calling getbalance can it display balances of 10^12 coins with a precision of 1 satoshi?), or is there a limit to the precision used?
It appears as if the official client is using qint64, so there will be no resolution past the decimal point.  The max value is bigger than Bitcoin's expected max.

Just use the same data types as the coins in question, and you should be ok.

You could use arbitrary precision for microbalances in your own app, but you won't be able to transfer them on the official blockchain.  Others might support arbitrary precision, but I haven't seen one yet that does.