Zopfli cannot handle PNG directly.
But you can use ehoeks-zopfli-png:
zopfli --png --i1000 logo.png
You will have to compile it:
git clone https://code.google.com/r/ehoeks-zopfli-png
./zopfli --png --i1000 logo.png
Note that this will only re-compress using the DEFLATE algorithm, you should optimize it first using other tools (OptiPNG, pngout, etc...) and other techniques (a bit off topic here, but check pngquant for smart lossy compression of PNG)
After compressing, you can still optimize it further using tools such as DeflOpt and defluff, but as far as I know this will only save a few bytes.
Another solution, windows-only, is PNGZopli, included in ScriptPNG alongside other tools. And there's also optipng-zopfli (optipng plus zopfli) but I haven't tried it yet.
Update: PNG support is being added in zopfli