All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If this company undertakes the task of minting the currency (making coins and printing money) against some amount paid by the government then there is no harm in it. It is a kind of manufacturing or hiring contract, both of which are allowed if Islamic principles are observed. The fact that a portion of the capital of this company is forbidden, does not prohibit dealing with it since the Prophet dealt with the Jews and others who did not avoid earning from forbidden means.
If the company, along with this practice, undertakes to reserve gold or other currencies equivalent to the currency which is minted, in this case, this reserve is considered a loan form the company to the government. If it is with the condition of paying an extra amount in addition to the principle amount, then it becomes an interest–based loan. The government has to pay back the loan but the minted currency is lawful because the loan of cash remains in the liability of the borrower and must pay back the original principle amount only, and may use it in any lawful means, such as to purchase a house, or mount or to mint a currency and the like.
Allaah Knows best.