The classic answer here would be Libya and Brunei, but I think Libya now has debt.
Brunei is a strange case in that it uses a joint currency with Singapore dollar, controlled by the monetary authority of Singapore, so in effect you can use Singapore debt as a substitute for Brunei dollar investment.
Not having any debt, and having a free currency is generally a bad idea, since you cannot control interest rates. Furthermore, if you can afford not to have debt, then people will be begging to lend to you at such favorable rates it would be foolish not to borrow a bit.
On the other hand there are many counties with no net debt. Singapore and Norway don't need to borrow but do so to provide bonds for the financial markets. They then invest the money they borrow. Norway can borrow so cheaply they can buy US treasuries and make a profit.