What can I do about pests the leaves of my Morning Glory vines?
Is there something I can spray them with that won’t harm the plant itself? I appreciate any ideas. 
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spray them down with horticultral oil
Probably juvenile beetles. You can purchase Neem Oil at farm supply or landscaping stores. You mix about 1 tablespoon in water in a spray bottle and spray it on (do under the leaves too). It is a natural insect killer that won't harm you or your pets. Repeat once a week until the damage stops.