Turkey (an official spoke at a celebratory rally, not sure if official congratulations were sent)
Tajikistan
Kyrgyzstan
Azerbaijan (given by their transportation minister on behalf of the president)
Brunei
Armenia
Hungary
Tunisia (new ambassador, may have been shamed into it)
Venezuela
Afghanistan (second vice president)
That's it. Out of 192 nations in the UN, Iran apparently gets congratulated by only ten.
Some Hungarians are upset about being in such company, so they made this poster:
Hezbollah's congratulations are ironic given the weak list of countries that are friendly enough with Iran to send a form letter:
Islamic Revolution Has Made Iran Pivotal Country in Region, World
Top UN officials also congratulated Iran.
Iranian media, trying to make these pathetic numbers look more impressive, are printing messages of congratulations from "analysts" like this one in Pakistan.
(h/t Stanley)