Late August through October is an ideal time to plant container-grown quince of either species. Not only does the cooler weather prevent stress from heat and drought, but the quince develops a healthy root system before next summer's intense sun arrives. Additionally, the plant's unestablished root system isn't straining to support flowers, fruit or spring growth. Don't worry about chilly weather; a container-grown quince continues to produce roots even when soil temperatures drop to 45 degrees Fahrenheit, and both fruiting and flowering quince are cold-hardy.
Spring planting is satisfactory for container-grown quince, and bare-root fruiting quince prefer an early spring planting time before any growth begins. Take special care with bare-root quince, as the harvesting process harms the root system and usually sends the plant into transplant shock. Although rare, a fruiting quince may be balled-and-burlaped or field-potted. These methods require nurseries to dig the quince from the field in late winter or early spring. Plant these in early spring when possible -- the dirt from the field isn't as rich as potting mix and won't support the quince through hotter months.
If you must plant a fruiting quince in summer, give the plant time to adapt to the future location. Unlike flowering quince, fruiting quince can't handle fast changes in environment and may suffer if moved from a sheltered nursery to a hot, sunny garden. If your garden is particularly exposed, move the quince gradually from partial shade to full sun, giving the plant a day or two to adapt at each step. Place a board or other barrier to shade the container. Black nursery pots quickly absorb summer heat, drying out root systems.
Fruiting quince produce relatively shallow root systems. Keep the quince well-watered but not soggy after planting until the root systems deepen. Watch for sprouts or suckers at the plant's base; disturbed roots often send up suckers after planting. Prune any suckers to ground level. Flowering quince are tough and adaptable, but may suffer from chlorosis in gardens with a high pH, such as soils in the West and Southwest. Amend alkaline soils before planting flowering quince.