You do not need any formal education to be good at writing articles for a newsletter. Now, it may be true that you may not be good at writing about every subject. Personally, I wouldn't even consider trying to write an article about the medical or legal professions, which I know very little about. But I do write what I know. Any experienced professional should be capable of writing about their field in a clear and compelling way.
The best way to write compelling copy is to pretend you are talking to someone on the phone who has asked you a question. That shouldn't be too hard. It probably happens to you all the time. Assuming your client's question didn't catch you completely off guard, consider what your answer would be. You were probably able to respond right away, providing helpful information that was valuable to your client. Just take that information and put it on paper the same way you related to your phone caller.
A great way to always have ideas ready for your newsletter is to quickly write down the questions you have been asked and a summary of how you answered it. Put those notes into your articles folder and when it is time to write your newsletter, you will already have the foundation for your next issue. Just add to that news of future events/seminars/workshops, interviews, customer of the month, book reviews, awards you have won or anything else that will help build your credibility. When you write as if you are having a conversation with your reader, you will have written a great newsletter.
Second, your newsletter will never get written if you don't set aside time to do it. Whether you schedule your writing time at 7am or 10pm is entirely up to you. Just choose a time at which you know you'll be able to do it to the best of your ability and without interruption. Turn off your phone, throw a 'Do Not Disturb' sign on the door or go to the office very earlier before anyone else gets there to interrupt you. However you do it, if you want to write, you must find and commit to a time that will enable you to focus.
Third, there are no good writers who don't read. In addition to making time to write, you must also make time to read. Read whatever you can to expand your knowledge and improve your writing. Pay not only to the content, but also the form and style. You'll need to read even more than you write in order to stay informed, inspired, and motivated. I have one entire table in my office filled with books and articles to read. For every hour I spend writing, I spent at least two hours reading and doing my homework to prepare for it.
One of the greatest benefits that you will receive from taking the time to read and write articles is this: it will make you a much better business person.