I noticed in the 1662 BCP there is included Coverdale's translation of the psalms, Why was this translation used instead of the psalms found in the 1611 AV?
The Psalter was not printed in the BCP 1549, 1552, or 1559. Cranmer treated the Psalms as a separate book, to be used with the BCP. Since the only Psalms available in solid translation were Coverdale's (Tyndale's had been rejected), that was the Psalter used alongside the first BCP. By the time 1662 came around, Coverdale's psalter had been used for more than 100 years. It seemed odd to separate it from the BCP, even if the AV was "better", and already 50 years old. Also, the Chants in the Parish Psalter (still used today) were familiar to every congregant. The Parish Psalter was fine using Coverdale's translation, so why opt for the KJV? That was the argument. Tradition won out, for the hearts of men cannot be indifferent to beloved things.