I got you fam.

So it starts with the term 'chilling' which means to hang out or spend time doing nothing in particular. You go to your homie's crib (house) and smoke weed, play video games. You're chilling.

This got changed to "cooling" (usually spelled coolin') which is semantically similar to chilling (chilled things are cool).

Lastly, this became "'boolin'," which is an ironic derivative of "coolin'." You see, many years ago in Los Angeles there were two rival gangs, the Bloods and the Crips, who despised each other. In particular, members of the Bloods would even go so far as to avoid any words beginning with the 'k' sound in Crips, replacing it with an initial 'b' [so instead of "coolin at the crib" one would "bool at the brib"]. This has now spread beyond a gang context to regular speech. It is often used in an ironic or incongruous fashion, such as here. You can't really hang out with a baby so the use of "boolin'" here has an additional ironic and humorous subtext.

Source: my friends were fairly serious drug dealers