There is definitely a whole suite of programs for you to do cosinor analysis. The most accessible being a web program developed by Dr. Reffinetti. You can find it here:
http://www.circadian.org/softwar.html
If you would prefer to use it with Matlab I have published some code that would be suitable in my eLife paper. If you are comfortable with Matlab feel free to adapt it to your needs or contact me and I can make it work for you. It is available on Github.
https://github.com/storchlab/Cosinor-FDR
As for the approximate entropy analysis I am unclear why that particular analysis is necessary? It can certainly be useful, and while appropriate for measuring (ir)regularity in a timeseries, I would argue that there are many other methods which can give you the same (or better) results with less limitations. Especially now that computationaly power is so cheap (i.e. you can do it on a desktop). Would you be willing to provide more experimental detail so I can point you in the right direction?