While not exactly NUC small, you can certainly build your own mini-PC using AMD parts. I currently use a small AMD build for my upstairs TV.
The Wesena HTPC-ITX4-v3 is a great case. Pair that with a picoPSU and external power supply for power and a micro-ITX motherboard, you can have a great system. The AMD Athlon 200GE is a great CPU for that build due to the low TDP (35W). A Noctua NH-L9a will keep things cool but also exceedingly quiet.
