An amicable divorce is a civil divorce. And a civil divorce is an uncontested divorce. Or, put another way, no contested divorce is amicable, nor civil.
A civil divorce is not a love-fest, and it does not mean that the husband and wife agree about everything. But they keep the disagreements within limits, and the two of them do not end up in court. No divorce that gets into the hands of lawyers and into court can be amicable or civil.
In an amicable divorce, the spouses usually do a lot of the negotiating themselves and can come to an agreement about the terms and conditions of child custody, child support, visitation, spousal support, and property division. After they agree on the terms and conditions, the couple can file the divorce paperwork. Often they can file pro se, with one of the spouses doing all the work (and without a lawyer).
Sometimes divorcing couples end their marriages through a collaborative divorce (where the two spouses and two lawyers collaborate with each other), a mediated divorce (where an unbiased mediator makes recommendations), or a pro se divorce. Regardless of the approach, divorcing couples can have an amicable divorce when they both commit to compromises rather than fighting about every issue. In a divorce, neither spouse gets everything he or she wants.