I found that being knowledgeable about what your state rules for cloth diaper a daycare are, and bringing in a modern cloth diaper, do a lot to convince them that it's ok.
I just brought one of my BG all-in-ones with me to show her how easy it was and that all she had to do was toss it in the provided wetbag. I also pointed out that it would be 8-10 less diapers taking up room and stinking up HER trash. Sold.
Re: Convincing daycare - anyone have links?
Link to a recent post:
https://community.thebump.com/cs/ks/forums/thread/49532554.aspx
It has some links and info.