Devious just to add my two cents. Always water in your plant in after it is transplanted. This will stop shock and it will help the roots recover from any stress. Also if the plant is root bound gently loosed up the roots. Personally, at the garden center we never remove soil from the roots. Just spread them a little so they grow outward after you plant them. Remember plants are living and smart they will root out on their own. Also if you are transplanting it might be a good idea to water in with a little bit of root stimulant just to give them a boost.
As for time of day I recommend waiting for a rainy or cloudy day if possible. If not do it after the heat of the day so the plant has time to recover before the next afternoon.
Coffee grounds would work great as a much but personally I dont think I would mix them in the soil. I would just sprinkle them about 1-1.5" thick over the top of the area where the plant is growing.