There are several models available to make the sort of decisions you are asking about. Most tend to make ordering decisions based on inventory level rather than on time: That is, they say things like "when the IL = 12, order 25" rather than "order 25 every 3 days".
The newsvendor problem is usually interpreted as a periodic-review model, so if you're looking for a multi-periodic model that is analogous, consider either the base-stock model or the $(s,S)$ model. Both assume that the period length is already fixed (e.g., 1 day). The base-stock model assumes we order every period, while the $(s,S)$ model assumes there is a fixed ordering costs, which means the orders are spaced out more.
The main model that uses order interval as a decision variable (i.e., focusing on time, not IL) is the $(r,T)$ model.
In continuous review, the relevant model is the $(r,Q)$ model, but I wouldn't exactly think of that as multi-period newsvendor, since it's continuous review.