As both a clownophobe and a non-Christian, I find the concept of the Clown Ministry both absurd and terrifying.
So what is meant by Clown Ministry? Nope, it's got nothing to do with Pat Robertson or the televangelistes. Back in the 1960's, a man named Floyd Shaffer decided that clowning could play a significant role in the Christian ministry, in terms of community outreach (specifically children and the elderly) and as a vehicle for morality plays. Apparently part of his justification for clowning as a legitimate religious expression is 1 Corinthians 4:10, "We are fools for Christ". This verse has since become the motto of the Clown Ministry movement.
The contemporary practice of clown ministry consists of a mix of community outreach through nursing homes, orphanages, and homeless shelters, and in-church skits either in a Sunday School setting or as part of a worship service itself. In both cases, the "gospel clown" is a childlike, innocent figure (think Parsifal) that is at once humble and happy. Typical skits cover a range of Christian topics, such as Christ's passion, forgiveness, loneliness, stewardship, grace, and reconciliation.
Although still employing the traditional elements of clowning (physical comedy, outlandish costumes, and typical clown props), clowns engaged in Clown Ministry are encouraged to bring joy and "build people up" rather than have fun at others' expense. A practical example of this is a variation on the standard clown gag trick involving a prop flower. Typically, the bright flower is offered to an audience member to sniff; when the flower is close to the audience member's face, the clown pulls a hidden trigger and the flower appears to wilt. In a gospel clown act, the trick would work the other way: the supposedly sunny, God-fearing radiance of the audience member would revive the previously wilted flower. You get the gist.
Most of these skits end with the gospel clown marking participants or audience members with a symbolic red dot on the cheek, called the "Mark of the Clown." Most practitioners of Clown Ministry include this red dot as part of their own clown makeup. Others use the famous Jesus Fish.
The seminal Clown Ministry handbook is Floyd Shaffer's "Clown Ministry," which provides the philosophical basis for religious clowning as well as practical tips for getting started with one's own ministry. Key chapters include "Interpreting the Scripture, Clown Style" and "Seven Myths of Hunger Skits".
The book is full of really... um, interesting interpretations and justifications for clowning as a religious instrument. I was particularly stricken by the discussion of clown makeup as symbolic of the Easter idea. Shaffer says that the whiteface base makeup of the clown is symbolic of death; when the clown then applies the red and black lines, symbolic of life, it is a reaffirmation of the journey from death to life. (I know that some Eastern cultures consider white a color of mourning, but I've never heard of red and black as being symbolic of life-- blood and death are much more standard symbolic interpretations.)
Other books on the subject of Clown Ministry include Philip Noble's "Fool of the Kingdom: How to Be An Effective Clown Minister" (which includes information on Gospel magic tricks) and Janet Litherland's "The Clown Ministry Handbook" (which focuses on how a clown may become a Gospel clown.)