We present a theoretical study of the charging effects in single and double layer black phosphorus quantum dots (BPQDs) with lateral sizes of 2 nm and 3 nm. We demonstrate that the charging of BPQDs are able to store up to an N max electron (that depends on the lateral size and number of layers in the QD), after which structural instabilities arises. For example, 3 nm wide hydrogen-passivated single layer BPQDs can hold a maximum of 16 electrons, and an additional electron causes the expelling of hydrogen atoms from the QD borders. We also calculated the addition energy (E_A) spectrum. For single-layer QDs with 2 and 3 nm lateral sizes, the average E A is around 0.4 eV and 0.3 eV, respectively. For double layer QDs with the same sizes, the average E_A is around 0.25 eV and 0.2 eV, respectively.