That's a complicated question for me because I have never written such types of essays but I have a piece of advice for you. When I had to write an essay I ordered it on https://essaysmatch.com/homework-paper/ So try to ask them if they write such letters.
Letter writing is an art. Not everybody can draft a good letter. Letters can be divided into two main categories i.e. Formal letters and informal letters. A letter by a coach to a college would come under the category of formal letters. There for you would have to follow the rules of a formal letter. These rules would include short sentences, tight mould, to the point language, cordial but impersonal style of writing and so on. It need not be very long unless the situation demands it to be. Come to the purpose of writing the letter without much dithering and end on a positive note. You would get several books and websites which would give you sample letters which might be useful as a reference while drafting your own letter. You can therefore check them out and improve your own letter.