A typical manipulation could occur around bed time. While the couple was together, the child's bed time was 8:30 P.M. One night, at Dad's house the child may ask “Why do I have to go to bed at 8:30 when Mom lets me stay up until 9?” Of course, Mom doesn't but Dad doesn't know that. Dad feels that he has to compete with Mom for the child's affections and says that the child can now go to bed at 9:00. The child then tries the same thing with Mom with similar success.
Of course, the answer is parents should communicate with each other and avoid competing for affections. A simple response to a child could be “I'll check with your mother and decide after we talk.” The child, knowing that the lie is about to exposed may simply fall back on “Never mind.” Of course, the best way to handle this is for parents to agree to check with each other on all such matters.
Another way of handling this is to explain to the child that there are two households with two sets of rules. So when the child explains that in Mom's house the child has a TV in the bedroom and can watch it until the child falls asleep, a good response is that there are two sets of rules. In Dad's house, there won't be a TV in the bedroom.