It all depends how these were constructed if your after the source file to re-size these peggy you may still loose quality with regards to the sharpness and clarity of the images. Your best bet would be to download them or ask the author directly as chances are they have posted or can retrieve the source file.
Either way, I'm almost sure there will be a loss of quality re-sizing from the .png source.
Hopefully the OP can post a link directly where he got them from which would help locate the author of these smilies which would yield a higher chance in getting the source files which would possibly (depending how they are designed) give off better results when re-sizing.
I still think these could be re-sized to 20px square and retain some kind of quality whilst limiting the breaking of the line format. It depends on what compromises you are willing to take but 10px square wuld be a good start in my opinion, even 24px which would be my personal maximum.
Thanks for your message. Unfortunately we don't have these icons in smaller sizes. The smallest size is 32x32. The icons are free for personal use and also free for commercial use, but we require linking to our web site. If you don't want to place a link, purchase them for $49 per set.
As for 18x18 size: we'll charge $2 400 ($80 per icon) to create the icons in this size.
VisualPharm - graphic design for software makers
You'll still loose quality whatever package you use. These are smilies which obviously started their life out in multiple layers where having the source file would give the ability to the user to re-size each layer accordingly and setting the blending modes to that size. Because it's png, all the elements are embedded on one layer causing the shift in size to really cause a low quality image.