I am trying to do my "days working in City allocation" for the City of Detroit, and TurboTax does not have the button indicated in the help.

Yes, if there is no wage income (W2) being reported for Detroit you will not get a prompt to allocate city wages. If your W2 does not show Detroit and local wages income in the local boxes (18-20) it is likely because there was no withholding.  If you are sure you owe Detroit City taxes (see below) then in the federal interview (Wages and Income) Edit your Detroit W2 and for boxes 18-20 select Michigan from the drop down enter the wages from box 1 in the box 18 and select Detroit for the locality.  

Now you can go back to your MI state interview and edit the city returns.  You should see the employer W2 show up and you can select "edit" in that line and the "Allocation by days" option in the dropdown on the follow on page.

Here is a link with information on Detroit City forms 5118, 5119 and 5120; for those who were either resident in Detroit all year, or non-resident but worked in Detroit or were city residents for part of the year.