To Coax

1. (obsolete) To fondle, kid, pet, tease.
2. To wheedle, persuade (a person, organisation, animal etc.) gradually or by use of flattery to do something.
3. To carefully manipulate into a particular desired state, situation or position.

(to fondle): caress, grope, touch up; fondle

(persuade gradually): cajole, canoodle, persuade, wheedle

(manipulate carefully into position): ease