We study the problem of designing dynamic double auctions for two-sided markets in which a platform intermediates the trade between one seller offering independent items to multiple buyers, repeatedly over a finite horizon, when agents have private values. Motivated by online platforms for advertising, ride-sharing, and freelancing markets, we seek to design mechanisms satisfying the following properties: no positive transfers, that is, the platform never asks the seller to make payments nor are buyers ever paid, and periodic individual rationality, that is, every agent derives a nonnegative utility from every trade opportunity. We provide mechanisms satisfying these requirements that are asymptotically efficient and budget balanced with high probability as the number of trading opportunities grows. Our mechanisms thus overcome well-known impossibility results preventing efficient bilateral trade without subsidies in static environments. Moreover, we show that the average expected profit obtained by the platform under these mechanisms asymptotically approaches “first best” (the maximum possible welfare generated by the market). We also extend our approach to general environments with complex, combinatorial preferences.