Hi Rose, I believe in using organic methods and usually don't recommend products I don't feel are good for the environment. So my first suggestion is to check out an Organic product made by Garden's Alive called 'Weed Aside.' I have used 'Weed Aside' and can tell you it works very well. You can find a link to them on the 'Market Place' page found on our 'Home' page. I buy most of our organic products through them, it is hard to find organic products in the stores. When you go to their web site send them a question if 'Weed Aside' will kill Ivy.
If you don't mind using non-organic you could use Round Up. You can either remove all the plants you want to save then spray the whole area or put the herbicide in a container and either "paint" the leaves of the ivy or wipe it on with a cloth. The ivy needs to be actively growing for these products to work. Don't cut them all the way down to the ground, leaves need to absorb the products. You could also put on form fitting rubber gloves and put jersey gloves on top of them, dip your fingers into the solution and then wipe it on the leaves with your fingers. Throw away the gloves and wash your hands thoroughly.
If you don't mind the extra work you could try digging all the ivy roots out of the ground being careful not to leave any roots. The soil would need to be sifted to achieve this.
Best Wishes, Diane