The latency and energy consumption incurred by I/O accesses are significant in data-centric computing systems. Computational Storage Drive (CSD) can largely reduce data movement, and thus reduce I/O latency and energy consumption by offloading data-intensive processing to processors inside the storage device. In this paper, we study the problem of how to efficiently utilize the limited processing and memory resources of CSD to simultaneously serve multiple I/O requests from various applications with different real-time requirements. We proposed SERICO, a system of scheduling computational I/O requests in CSD. The key idea of SERICO is to perform admission control of real-time computational I/O requests by online schedulability analysis, to avoid wasting the processing resources and memory capacity of CSD in doing meaningless work for those requests deemed to violate the timing constraints. Each admitted computational I/O request is served in a controlled manner with carefully designed parameters, to meet its timing constraint with minimal memory cost. We evaluate SERICO with both synthetic workloads on simulators and representative applications on realistic CSD hardware. Experiment results show that SERICO significantly outperforms the default method used in the CSD device and the standard deadline-driven scheduling approach.