There is no simple direct conversion but you can calculate a peak flow using TR-55 and then using that flow solve Q=CIA for an equivalent "C".

I would not do what RWF7437 recommends.  TR55 and Rational will almost always give vastly different Q values, as they have different applications.  Usually, I use Rational for small areas (10 acres or less) with a higher percentage of development.  Over 10 acres and Rational underestimates, I think.  I use SCS methods for mid-sized areas which are more natural and/or agricultural.  Anything over 0.5 square mile and TR55 vastly overestimates in my opinion.  Try a flood model (HEC or PSU4) above 0.5 square mile.

If you must convert CN to C, Rossmiller's Conversion can be applied.  It is a monster equation, but here it is:
C=(7.2*(10)^-7)*(CN^3)*(RI^0.05)*{[(0.01*CN)^0.6]^-s^0.2}*[(0.001*CN^1.48)^(0.15-0.1*I)]*{[(IMP+1)/2]^0.7}, where RI=return interval(yr), IMP=impervious coverage( decimal)and S=average land slope (whole number percent).  I have a spreadsheet which I have used (and has passed reviews) in the past, but it has not been QC'd by another engineer.  If you leave your email address here, I will send it to you to play with.

Iha has the correct solution. Rossmillers formula was developed by Ron Rossmiller, formerly of Univ. of Iowa. I have included it in my software for use in the rational formula method for computing runoff and call it, of course, Rossmiller Rational. CN in the main formula is computed by the formula CN=98IMP+X(1-IMP).
IMP = % Imperviousness, dimensionless decimal
X= factor based on soil type
Type A=39
Type B=61
Type C=74
Type D=80
The antecedant moisture condition is assumed as II

Iha, I am interested in your spreadsheet.  my email address is jwledy@apexse.com

I sent it to jwledy@apexse.com this morning, it came back server unknown.  There is a nomograph available for this conversion.  I know it is Page 29 of PennDOT/FHWA's PSU-IV, and probably other places.

IHA,

I would be interested in your spreedsheet as well.  If you don't mind of course.

murrisonenvironmental@cox.net

Thanks
Scott Murrison

Just a clarification, Dr. Ronald Rossmiller taught at Iowa State University - not the University of Iowa. A small point if you live outside of Iowa, but a huge issue for those of us who live in Iowa. ;)