They best way to phrase your idea in this situation would be "Rahim is applying for admission to that coaching center." The phrase you have "we wanted to" is incomplete and you'd have to add something to the end (such as "...that coaching center that we wanted him to go to."), get rid of it completely, or rephrase the sentence to express the "we" part of your idea.
In typical cases, when someone is saying "he is being admitted..." it usually is the context of hospitals (e.g. "He is being admitted to the emergency room for his wounds."). It's true. Unless you know that he is currently in the process of being admitted to the coaching center (i.e. they are filling out the paper work to admit him), the present progressive form is not the most appropriate. However, you're message is still coming across, and the idea is totally conveyed!