This was a civil court case so there wasn't a prosecutor. There was a plaintiff and a respondent with their counsels. The original Plaintiffs were the citizens and tax payers of Jefferson County, AL
I couldn't find the original attorneys on a quick search but these are the ones who argued before the Supreme Court on the appeal.
W. McLean Pitts argued the cause for appellants in No. 23 and for appellees in Nos. 27 and 41. With him on the briefs were Joseph E. Wilkinson, Jr. and Thomas G. Gayle.
David J. Vann argued the cause for appellants in No. 27. With him on the brief were Robert S. Vance and C. H. Erskine Smith.
John W. McConnell, Jr. argued the cause and filed a brief for appellants in No. 41.
Appellee Richmond M. Flowers, Attorney General of Alabama, argued the cause pro se. With him on the brief was Gordon Madison, Assistant Attorney General.
Charles Morgan, Jr. argued the cause for appellees in No. 23. With him on the brief for appellees Sims et al. was George Peach Taylor. Jerome A. Cooper filed a brief for appellees Farr et al.
Solicitor General Cox, by special leave of Court, argued the cause for the United States, as amicus curiae, urging affirmance. With him on the brief were Bruce J. Terris and Richard W. Schmude.
Briefs of amici curiae were filed by Leo Pfeffer, Melvin L. Wulf, Jack Greenberg and Robert B. McKay for the American Jewish Congress et al., and by W. Scott Miller, Jr. and George J. Long for Schmied. President of the Board of Aldermen of Louisville, Kentucky.
Hope this helps.