are you saying you have a data set that you expect can be modeled by $\dfrac C {1+e^{a t}}$ and you want to estimate $a$ and $C$ from a least squares fit to your data?
You cannot on a direct way. Use a non-linear method of regression : Nonlinear regression - Wikipedia, the free encyclopedia
Nevertheless, it can be transformed to a linear regression thanks to a method using an integral equation, paper published on Scribd : Régressions et équations intégrales
page 17 : see the computation in the case y=a+b*exp(c*x)
To apply in your case : l=C/(1+e^(A*t)) , let y=1/l ; a=b=1/C ; c=A
The publisched method requires to be slightly adaped in the particular case a=b. Contact me if you intend to try this method.