The integration of solid-state single-photon sources with foundry-compatible photonic platforms is crucial for practical and scalable quantum photonic applications. This study explores aluminum nitride (AlN) as a material with properties highly suitable for integrated on-chip photonics and the ability to host defect-center related single-photon emitters. We have conducted a comprehensive analysis of the creation of single-photon emitters in AlN, utilizing heavy ion irradiation and thermal annealing techniques. Subsequently, we have performed a detailed analysis of their photophysical properties. Guided by theoretical predictions, we assessed the potential of Zirconium (Zr) ions to create optically addressable spin defects and employed Krypton (Kr) ions as an alternative to target lattice defects without inducing chemical doping effects. With a 532 nm excitation wavelength, we found that single-photon emitters induced by ion irradiation were primarily associated with vacancy-type defects in the AlN lattice for both Zr and Kr ions. The density of these emitters increased with ion fluence, and there was an optimal value that resulted in a high density of emitters with low AlN background fluorescence. Under a shorter excitation wavelength of 405 nm, Zr-irradiated AlN exhibited isolated point-like emitters with fluorescence in the spectral range theoretically predicted for spin-defects. However, similar defects emitting in the same spectral range were also observed in AlN irradiated with Kr ions as well as in as-grown AlN with intrinsic defects. This result is supportive of the earlier theoretical predictions, but at the same time highlights the difficulties in identifying the sought-after quantum emitters with interesting properties related to the incorporation of Zr ions into the AlN lattice by fluorescence alone. The results of this study largely contribute to the field of creating quantum emitters in AlN by ion irradiation and direct future studies emphasizing the need for spatially localized Zr implantation and testing for specific spin properties.