This confusing word pair appears to be difficult.  But, it is really a simple fix.  This word pair is confusing because of the spelling. Let’s look at the sounds in the words.  I think that you will be surprised.

COAT is pronounced K, long O, T

QUOTE is pronounced K, W, long O, T

The only difference in these words is the W sound on the QU.  The spelling “QU” is always pronounced as KW.