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A fiat-backed stablecoin issuer earns seigniorage by investing par-value liabilities in short-term Treasury securities that carry a convenience yield. Because the issuer has grown large relative to the Treasury-bill market, its reserve demand is no longer price-taking: additional issuance increases bill scarcity, raises the nonpecuniary convenience yield embedded in bills, and thereby lowers the pecuniary reserve return that funds issuer seigniorage. I embed a Krishnamurthy and Vissing-Jorgensen convenience-yield schedule inside a monopolistic private-money issuance problem in the tradition of Klein and of Li and Mayer, in a two-period, two-maturity setting with money-in-utility households whose stablecoin holdings substitute for bank deposits. Three results follow. First, the endogenous convenience yield acts as a stabilizing force: the monopolist internalizes its own price impact, so the issuance feedback loop converges rather than amplifies, and equilibrium issuance is strictly below the price-taking benchmark. Second, a reserve-maturity cap of the kind imposed by the GENIUS Act of 2025 confines the issuer to the short end of the curve, where the convenience-yield schedule is steepest; the cap therefore raises the marginal convenience cost of issuance and contracts equilibrium supply, while insulating the long end from further scarcity. Third, comparative statics deliver signed, testable predictions linking household money demand, the reserve cap, and the equilibrium Treasury-bill convenience yield. The model rationalizes the small but non-zero yield effects estimated by Ahmed and Aldasoro and clarifies when prudential reserve rules trade issuer scale against safe-asset price stability.