To find the right black ink cartridge for the HP Envy 6010e All-in-One printer, you can use the HP 305 XL black ink cartridge. This cartridge has been specially developed for the HP Envy 6010e and other compatible models. Alternatively, you can also consider compatible cartridges from other manufacturers such as Prindo Green XL, which are also compatible with the HP Envy 6010e.