Hey Bud.. In all likelihood your cherry has a different rootstock than what you want to graft unless your doing bud grafting. I wish I could be more help but grafting is just out of my knowledge base. lets say you wanted to come as closeas possible to cloning a cherry. You would have to buy rootstock for the size tree you want whether it be dwrarf or as big as a standard from someone like Raintree Nursery. You would then graft a whip from the cherry your looking to multiply onto the purchased root stock.
There are some hardwoods you can air layer if you don't care what the root stock is. I don't know if the "prunus" family falls into that category. I'm sure an expert working in ideal conditions could do leaf cutting but way way out of my skill set.
Rock on bud and I can usually provide a better answer when it comes to gardening but that's just way to tough.