I'd be tempted to do this two-pronged.  First, I'd send an e-mail to the other budget holders (or specifically to the one floor that continues to come up and get yours) requesting a reminder go out to the floor about the procedures and that if other supplies (diff brand coffee, creamer, etc) is desired that the employees should see that person.  And yes, I would state that if your floor continues to provide the supplies for their floors, then the budget will be adjusted accordingly to accomodate the added expenses for your floor supplying coffee for 2 floors.

Then I would put a notice up, like you stated, saying that coffee and supplies are for this floor employees only and not to be taken to other floors.  Then I would list the appropriate contacts for each floor for them to go to if they have any requests for coffee supplies on their floor.  Under this, you can always put the explanation that yes, you all work for the same company, but the budget is broken down by floor for certain stuff and the coffee supplies are one of those, and they are in essence misappropriating budget items when they take what was allotted for your floor to another floor for consumption (use).  Drastic, but I'm pretty sure that the employees doing this are not aware of the way the coffee fund is allocated and are not thinking it's that big a deal.  Giving them the information, especially on who to go to on their floor to discuss the selection, might really solve the problem.

Another option would be to put a coffee can out and run an honor-system cost/payment for folks who are not on your floor.  We had a coffee station in our office, which was paid for by a group of folks all in the "coffee fund" group.  They all paid a set amount each month, and for that money, got to drink coffee for free and their preferences were purchased.  If anyone not in the coffee fund group wanted a cup of coffee, they could either join (paying the monthly due) or they could put $0.55 in the coffee can per cup of coffee they drank.  This money, along with the monthly dues, is what was used to purchase the coffee and supplies.

No matter how you address this, someone somewhere will think you're being petty.  The thing to remember is that you are not... you are trying to be fiscally mindful for your department/floor and need to stick to your guns.  Let us know how this works out over time.