You can only install two black ink cartridges if your printer uses two different types of black ink. If you are trying to install a black ink cartridge in a color cartridge slot, your printer will not function and you could potentially cause damage to the machine.
Some photo inkjet printers require two black ink cartridges to print text and more defined shades of black in your photos. With these printers, like the Canon PIXMA TS5020, you need to install two different black ink cartridges. For example, the TS5020 uses the PGI-270 black ink cartridge to print text and the CLI-271 black ink cartridge to enhance the black in your photos. Printers that work with two different black cartridges will have designated cartridge slots for each cartridge. Make sure that you are installing the correct cartridge number in the appropriate cartridge slot!