The first tip for telling a vendor you don’t have money to pay them? Never get yourself in the situation in the first place. If you hire someone to do work for you, you need to pay them. If you don’t? They can sue you for nonpayment of services.
That being said, perhaps you don’t have the money to pay your vendor in a timely fashion, but you do intend to pay them when you get the money. Admittedly, I had this issue with paying some of my writers earlier this year when I was chasing down a client who owed me a sizable amount of money for a rather large writing project we did for them last year. The client hadn’t paid me yet, but since I’d had the money in my account at the time, I paid my writers for their work on that project anyway. The problem cropped up when more and more projects came in and I fell behind on getting paid by the clients who were giving us all that work.