Wouldn't it be different based on whether the year had leap days in it?
You might be able to ask the user for a year, then try and calculate the date by comapring the value given as DayInYear versus FirstDayOfMonth(CreateDate(<year>,<month>,1).
Something like:
<cfset daysinyear=100>
<cfset currentmonth=1>
<cfloop condition="daysinmonth less than #DaysInMonth(createdate(year,currentmonth,1)#">
<cfset daysinyear=daysinyear-#daysInMonth(createdate(year,currentmonth,1)#>
<cfset currentmonth=currentmonth+1>
</cfloop>
The date is #currentmonth#/#daysinyear#/#year#