Single-photon cameras are becoming increasingly popular in time-of-flight 3D imaging because they can time-tag individual photons with extreme resolution. However, their performance is susceptible to hardware limitations, such as system bandwidth, maximum laser power, sensor data rates, and in-sensor memory and compute resources. Compressive histograms were recently introduced as a solution to the challenge of data rates through an online in-sensor compression of photon timestamp data. Although compressive histograms work within limited in-sensor memory and computational resources, they underperform when subjected to real-world illumination hardware constraints. To address this, we present a constrained optimization approach for designing practical coding functions for compressive single-photon 3D imaging. Using gradient descent, we jointly optimize an illumination and coding matrix (i.e., the coding functions) that adheres to hardware constraints. We show through extensive simulations that our coding functions consistently outperform traditional coding designs under both bandwidth and peak power constraints. This advantage is particularly pronounced in systems constrained by peak power. Finally, we show that our approach adapts to arbitrary parameterized impulse responses by evaluating it on a real-world system with a non-ideal impulse response function.