Note that manual installation of Biblatex and Biber is not recommended except in exceptional circumstances.
Such circumstances include:
you've been bitten by a bug which is fixed in a newer version, you need the fix urgently and you will remember to undo the manual installation at the appropriate time (and you'll recognise when that is);
you have been foolish enough to update your TeX distribution right before a deadline, have no roll-back plan and the update has broken your bibliography, you plan to fix the real problem after the deadline and will remember to undo the manual installation at that time.
In all other cases, the best course is to update your document or other packages to use the new Biblatex/Biber or to wait for the fixed version to be available through your normal update routine.
Note that there is no guarantee that rolling back Biblatex/Biber will work with an updated TeX distribution, although it is likely in most cases to work in the short term.
Caveat emptor ...
If you are sure you want to do this, then proceed as follows. These instructions assume you are using TeX Live on a Unix-ish system (Mac OS X, BSD, GNU/Linux etc.).
You need to download matching versions of Biber and Biblatex from SourceForge: Biber and Biblatex.
At the command line (e.g. Terminal for OS X users), navigate to the directory you downloaded the files to.
ls *.tgz *.gz
should show you a file named biblatex-<version>.tds.tgz and another named biber-<arch>.tar.gz where <version> is the version you need of Biblatex and <arch> matches the architecture of your OS.
mv biblatex-<version>.tds.tgz $(kpsewhich -var TEXMFHOME)
pushd $(kpsewhich -var TEXMFHOME)
tar -xzf biblatex-<version>.tds.tgz
kpsewhich biblatex.sty
The last command should return a file in you personal TEXMF tree and not in the main TEXMF tree. It should be somewhere in your home directory.
popd
mkdir -p ~/bin
tar -xzf biber-<arch>.tar.gz
This should produce a biber binary, possibly in a sub-directory.
mv <sub-directory>/biber ~/bin/
To use your downloaded copy of Biber, use ~/bin/biber <filename> rather than biber <filename>, to make sure you get the correct one. (You could adjust your PATH to automate this, but it is not worth it for a very short-term temporary workaround.)
biblatexmanually. For Biber it should be enough to place it somewhere in the PATH so it can be picked up your system automatically. (If you already have Biber installed somewhere, you can of course just overwrite it with the downgrade file.) – moewe Jul 26 '16 at 07:52PATHso that it is found before the version installed by TeX Live. @ OP Are you about to submit or close to a similar deadline? If so, this kind of workaround makes sense. If not, it would be better to update the templates. Did you delete MacTeX 2015 when you installed MacTeX 2016? If not, you can just switch back to the 2015 version. – cfr Jul 26 '16 at 12:47biblatex; I should have thought about it a bit longer, though, ... updates could be a major problem. – moewe Jul 26 '16 at 14:47biblatexin your local texmf tree as described in the links above (if you have trouble with that, please specify exactly what you tried and how it didn't work for you). Biber you should place in the PATH (so that it is found before the current version of Biber from TeX Live), how to do that I cannot tell you since I don't use a Mac (maybe you can find info on that elsewhere on the web, here, for example, the commandwhichcan help you). – moewe Jul 26 '16 at 15:18echo $PATHgive? – cfr Jul 26 '16 at 15:19tlmgrsave backup copies of packages so that individual packages can be rolled back. So, really, the 'feature' you are requesting pretty much exists already for both major upgrades (new edition) and minor ones (tlmgrupdate). TeX Live Manager is just a wrapper fortlmgr, so I assume it saves backups by defaults, unless MacTeX uses a custom configuration. – cfr Jul 26 '16 at 15:28