URGENT! Please help me with puppy housebreaking question?

My puppy is about 10 weeks old. I am working on housebreaking him. I take him out through the same door to the same spot on the same path every time to eliminate. The problem is that, as soon as I set him down to do his business, he does not stay at the designated spot, runs away and begins to eliminate elsewhere (after a long time of sniffing around). Having him eliminate anywhere else besides the prepared spot is not an option, but I am still working on leash training him, and he does not yet recognize his name. I am at a loss of how to get him to stay in his spot, so I can positively reinforce him when he goes. His elimination spot is a rocky area, in a yard with a gry lawn and a garden, in which I need to teach him not to eliminate. There is no way to fence in the spot. I have already tried putting his stools in the spot, to no avail. Please help me figure out how to get him to stay long enough in the right spot to eliminate! Thanks in advance for your help! :)