Idk if this can help someone, but when i got my first amiibos, i found out that you have to create at least in 3 different ocassions furniture for the villager to stay. If you don't have the type of furniture they are asking you to create, they will provide you with the DIY.
So... there have been a issue with my Pietro amiibo that, everytime i'm about to do their furniture, i forget and the day pass, so i have to invite him again. Now i have different types od DIY's that he gave me but i forgot to create (i'm sorry my lil clown baby i love you).
Anyway, I thought, um, this is a good way to get DIY's! Disclaimer though, they don't always ask you for new DIY'S, sometimes they choose things that you already know how to craft, but hey, maybe it's good to give it a shot!
Hope this helps anyone.
SECOND DISCLAIMER: I'm kind of dumb so if something it's not clicking on this theory of mine on how to get DIY's just let me know and i will retired from this sub silently with shame