Yes, it is permissible to accept money for teaching Qur’ân, particularly in case of need. In Sahîh al-Bukhârî  it is related that the Prophet (peace be upon him) said: “The best money you can earn is that which you earn through Allah’s book”.
This is the saying of the majority of the people of knowledge, including the great jurists Mâlik and al-Shâfi`î. It is also one of the opinions narrated from Ahmad b. Hanbal.
There is another hadîth that forbids such earnings, but it is a weak hadîth.
I hold the opinion that it is lawful to earn money for teaching the Qur’ân and the Sunnah and for imparting Islamic knowledge, since it is clearly sanctioned by the above-mentioned hadîth.
And Allah knows best.