Hi Numaggie, Rhodo's and Pieris are both acid loving shrubs, so I hope it's an acid soil to where your moving them to.
I think the ideal time to move them would be in the autumn but the main point to remember is try to avoid to much root disturbance, you can achieve this by digging a large a root-ball as you can manage to handle with as much soil
clinging to the roots as possible.
Secondly keep the roots moist at all times of transplanting, wropping the roots in damp hessian sacking is a good idea with an outer wrapping of polythene to keep in the moisture.
When it comes to planting add plenty of ericaceous compost to the hole and also save some as a mulch and give them plenty of water for the first year at least.
Good Luck. Tbird+