The Rhododendron genus contains about 900 species, including deciduous plants (usually called "azaleas") and evergreen plants (commonly called "rhododendrons"). The genus Paeonia also contains a number of species, but the most common garden types are herbaceous peonies (Paeonia lactiflora) and tree peonies (Paeonia suffruticosa). Compatibility between peonies and rhododendrons depends on finding species and cultivars of have similar cultural requirements. Be aware that both peony and rhododendron plant parts can cause gastric distress if ingested.
Though some rhododendrons can tolerate full sun, many, like native Catawba rhododendron (Rhododendron catawbiense), hardy in U.S. Department of Agriculture plant hardiness zones 4 through 8, are natural woodland understory plants that succeed best in partial shade. Rhododendrons require well-drained soil that is on the acid end of the pH spectrum. Poorly drained sites often cause rhododendron death. The plants are shallow-rooted and should not be planted deeply. They are also water lovers and must receive supplemental water during dry spells. Mulch around the plants' bases, but do not allow mulch to touch the trunk.
Garden or herbaceous peonies, like the time-honored "Festiva Maxima" variety (Paeonia lactiflora "Festiva Maxima"), hardy in USDA zones 3 through 8, generally thrive in full sun to very light shade, but full sun produces the most flowers during the May bloom period. Blooming in April and May, tree peonies, like white-flowered "Godaishu" (Paeonia suffruticosa "Godaishu"), hardy in USDA zones 5 through 8, also require full sun to light shade, but they're more shade tolerant. Well-drained soil is a must for both peony species. Tree peonies may also require some protection from wind.
Peonies generally need more sun than rhododendrons, but the plants from the two genera could be placed in close proximity in a garden that features areas of full sun and areas of light shade. Evergreen rhododendrons are a suitable match for peonies, providing interest when garden peonies have died back in late summer. The larger plants also act as windbreaks for the wind-sensitive tree peonies. Many rhododendron species and hybrids, like the white-flowered "Album" variety (Rhododendron catawbiense "Album"), hardy in USDA zones 4 through 8, grow to be quite tall and should be placed behind the shorter peonies.
For small spaces or containers, pair compact "Yaku" rhododendron (Rhododendron yakushimanum), hardy in USDA zones 5 through 9, with a classic garden peony like "Sarah Bernhardt" (Paeonia lactiflora "Sarah Bernhardt"), hardy in USDA zones 3 through 8. Both have showy pink flowers and grow about 3 feet tall. Those with larger spaces might want to try a pairing of two pink-flowered varieties, "Maxecat" (Rhododendron "Maxecat"), hardy in zones 5 through 8 and somewhat more sun tolerant than other rhododendrons, and the old fashioned peony "Lady Alexandra Duff" (Paeonia "Lady Alexandra Duff"), hardy in USDA zones 3 through 8.