According to Nikon USA...the SB400, SB600, SB700, SB800, SB900 and SB910.
I didn't see anything that said it was I-TTL only...so perhaps you can find a smaller used flash like the SB23, SB22/SB22s, SB-30 to add a bit more light. I can't seem to find anything definitive. Sorry.
#3. "RE: Does the Flash Nikon SB-N7 works well with the P7100 Nikon Coolpix?" In response to Reply # 2
Rancho Cordova, US
It seems that Nikon have finally integrated TTL within the Coolpix lineup with accessory speedlights (YAY!) and older (read: film era) speedlights can be used in Manual or Auto (letting the speedlight determine flash exposure) modes.
#5. "RE: Does the Flash Nikon SB-N7 works well with the P7100 Nikon Coolpix?" In response to Reply # 4
Yes the SB-400 is the perfect size for a small camera.
Just a small caution - using the SB-400 you will not be able to set it to "Master" and control other speedlights. The P7X00's are not able to control other speedlights with their built-in flash but if one of the higher spec speedlights is fitted to the camera then you can control remote speedlights.
If you are not planning on controlling other remote speedlights then I think you will be happy with the SB-400.
Regards, Clive Liddell Pietermaritzburg South Africa