Postmates is a great delivery service, but at least in Seattle they cannot handle certain types of special deliveries, such as the delivery of alcohol or tobacco. It was explained to me as a licensing issue. For similar reasons I doubt they'd be willing or able to handle cannabis at the moment.

I could imagine this changing in the future. I heard that Postmates can deliver alcohol in California; and Amazon Fresh can deliver alcohol today in Seattle. But I suspect there would be many barriers to overcome for cannabis delivery (assuming it can be done lawfully at all).