To think the request is muttar, since one is even allowed to think about melacha on Shabbos (though one is not allowed to talk about melacha, like saying “I will buy something after Shabbos”).
If it’s a spiritual request (like shidduchim, which is a mitzvah since getting married and raising a family of ovdei Hashem is a mitzvah), there are opinions that you can pray for that on Shabbos. Other opinions forbid even this. The minhag is to be meikel, and so ruled Rav Belsky.