I have heard of leaf-bud cuttings being used on some varieties of rhododendrons. They contain the leaf blade, the petiole, and a short piece of stem containing an axillary bud. They are taken from semi-hardwood cuttings that are not dormant. They are done with a rooting hormone much the same as stem cuttings: insert bud ½ -1" into sterile media, use mist and bottom heat.

Stem cuttings are the most common method of propagating rhododendrons. When stem cuttings are not commercially viable, then tissue culture is used.

Here is a link that might be useful: Rhododendron propagation

Rhodyman,
Thanks for the very useful information. I'll certainly try some of these methods and hope I'll be more successful in the future.