cover letter for rental application

Has anyone ever written one for rental or received one if they're landlord?
I was looking up rental tips and this was suggested.
I have been having some difficulty finding somewhere to rent in my area in my price range, and there is also competition which I'm losing out on.
I feel being a single mother where 30% income is based on child support/ FTB/ parent pension puts me at a disadvantage over those who apply with 2 incomes. I have glowing references from my current real estate, tenant ledger which shows on time every month with rent yet still can't seem to get anything.
Hoping to try out this letter thing and hope to give myself an advantage.
I'm just not sure what to put and how to word it.
What do others think or have done?

as a landlord I always try to pick a nice family (if I have a choice) and a cover letter would be a nice touch

Yep. It works well. We put info about past rentals and how we treated them, a little family info, work, and future plans...... Aims you have for the future.
Just brief though. I think if you say things about living in the area for a long time it helps.
I felt strange doing it, but it does work.
We had pets so we also included a bit about their excellent behaviour.

Thanks guys glad to hear positive feedback. I felt weird about doing it but if it gives me a boost will just do it.

I do it when I really really want a house, and tailor it specifically to the house. It's worked every time.

We did it for this house, we were up against people that were employed - dh is a student and I'm a sahm. We were honest and up front with them and they must have appreciated it because we got it.

This is an interesting idea. Im going to be looking at houses to rent in the next few months and Im a similar boat.
Anything that helps is great :)