Look it up in any dictionary. There is a singular form only. There is no plural. Divorces are not "performed". They are mandated by a court order. As I said before, a divorcer is the person who initiates a divorce (that is why there is no plural).
divorcer
\Di*vor"cer\, n. The person or cause that produces or effects a divorce. --Drummond.
Source: Webster's Revised Unabridged Dictionary, é 1996, 1998 MICRA, Inc.
Since actually being in the dictionary is a prerequisite for being a dictionary word, I think it is fair to say this is not.