A couple of months back I carried on an istikhaara for marriage and the result of that istikhaara was not in my favour. I would like to carry out another istikhaara for the same purpose ( for the same girl ). What is the procedure for such a matter? Is there a sadqah to be paid?

This is not wajib it’s up to you either you give Sadaqa or not.
But what does Istekhara mean? Why and when do we do this? Normally we do Istekhara when we are totally confused and stuck between two options or even for one specific task that do I do this or not.
But in your case it shows that your it seems that you wish to marry with that particular girl and in this issue you have no confusion rather you have a kind of fear. Don’t be scared just rely on Allah as Allah says in the Holy Quran:
‎وَشَاوِرْهُمْ فِي الْأَمْرِ فَإِذَا عَزَمْتَ فَتَوَكَّلْ عَلَى اللَّهِ إِنَّ اللَّهَ يُحِبُّ الْمُتَوَكِّلِينَ

…..and take counsel with them in the affair; so when you have decided, then place your trust in Allah; surely Allah loves those who trust.(3:159)