A non-profit can put money into a C-corporation that it owns under the same circumstances as a private shareholder could, because an investment in a C-corporation is simply a passive investment which a non-profit is permitted to make (subject to various exceptions and special cases that rarely apply).
It can either purchase new shares in the C-corporation for cash, or can loan money to the C-corporation.
If it loans money to the C-corporation, it should do so in a formally documented transaction at a rate at least equal to the minimum rate that does not result in deemed gift, set forth at 26 U.S.C. § 7520 of the Internal Revenue Code, and really, should do so at a fair market value interest rate, if that is higher (which it almost always would be the same as or higher by definition due to the way that the Section 7520 rate is determined).