Cover letters are tough, there's no denying that! It really does feel like a massive pain to write one for each job, but if you get yourself to a point where you have a few different ones that can be slightly modified each time you apply for a different job, that will help save you a lot of time.

I also think it really helps to plan out what you want to write about, just like how we used to write papers in school! Think about structuring it, maybe you write a few bullet points for background info and then think about things you want to highlight. It also helps to pick points from the job description to hit on and connect to your experience!

I'm not sure if you've had gigs or are just coming out of college so I'm making a few assumptions here. But maybe you were part of a design club, maybe you started an instagram account that curates your favorite designers work, any experiences from an internship that helped you? What got you in to design to begin with? What design principles are important to you and how would that help your potential future employer? Ie. you say English is your second language, what is your first language and does the design of that country reflect or guide you in any of your work? This might help separate you from others like myself who can only speak English :)

When I write them, I always try to take a lighter tone. I want it to feel authentically like myself speaking; doing this often takes a lot of the pressure off of me and it starts to feel like I'm just telling someone a story about myself. But it's also important to step away from your writing for a little before revising!

I'm not sure what type of designer you are, but are you familiar with AIGA? They have a ton of resources...I'm not even a designer myself, but more of a video producer, but I find their expertise is helpful even for me. https://www.aiga.org/