For the Festival of Music type of competition where the users would be free to chose any country to represent (I would suggest letting users choose even those countries that are regularly represented in TISC), I would use this system to avoid conflicts:
First every user who wants to participate makes their list of songs they would like to submit in a preferential order. They would be free to have any number of songs from any number of countries on their list.
Then if there isn't a conflict, meaning that a user has a country as their #1 choice that no one else has as a #1 choice, then that user gets to represent that country and song.
If there's a conflict, meaning that two or more users want to represent the same country with different songs, the host would decide with a draw. The user who won the draw would represent the country with their selected song, and the user(s) who lost it would go on to the next round....
Where all the users who didn't get to represent their #1 choice would have chance with their #2 choice. If the country of their #2 choice was already taken in the previous round, or they lose the draw once again in a conflict, they would go on to the third round with their #3 choice.
This goes on until either everyone gets a country+song, or the users left without a country ran out of options on their list. If the latter happened, we would have another similar selection process for these users if they still wish to participate.