Thinking about the chemistry of it, I doubt you could get the weed psychoactives to dissolve in the coffee water. Barring the use of strong alcohol instead of water in your coffee maker (and idea which certainly has potential, although you'd need to adjust the heating parts to avoid vapour lock from the lower boiling point of the ethanol, and entirely possibly change some electrical components for fire safety) I would say the best approach would be making an equivalent of cannabutter with cream (non-dairy coffee creamer might work, but I have no idea what's in it other than that one mythbusters episode with the coffee creamer cannon thing) and then using that in your coffee. Kinda sucks that you can't make black coffee, which is the true coffee at least when you're not at costa, with weed infusion easily though. You could probably make an irish coffee with bonus weed, although I'm not exactly sure how making weed tincture works as it's not something that's ever interested me.
Maybe if you used some kind of surfactant, preferably one that wouldn't make the whole thing taste like soap, you could get some degree of extraction from the weed into the coffee? This is really getting far past my chemistry knowledge though, I'd have to find a chem student that smokes and ask them.