Instant delivery has been one of the essential location-based services in modern society. In order to achieve timely and efficient instant delivery, the present works often formulate the problem as a Traveling Salesman Problem and use delivery programming to find a near-optimal solution to the problem. The corresponding solutions, while achieving high efficiency, may leave little room for unexpected delays in each delivery task. Because of the strict deadline requirement for instant delivery, such design may lead to delivery overdue, especially with dynamic traffic and unexpected occasions during the delivery. In this paper, we propose a delay-tolerant Dynamic Scheduling scheme for Instant Delivery (D-SID). By explicitly accounting unexpected delays and exploiting opportunistic relays, the scheme can improve the delivery reliability under dynamic environments. The simulation results show that with D-SID, the overdue delivery ratio is significantly reduced compared to the traditional scheduling that maximizes the number of tasks.