Onsen that allows tattoos?

My partner and I are both tattooed, he almost has a complete sleeve and I have quite large ones that also won’t be able to be covered with patches.
I’m also not really keen on going to an onsen where I would be without him (gendered onsen for example) as I have pretty bad anxiety and body image issues.

Looking for recommendations for potentially private onsen experiences, and if anyone knows of any natural onsens that you can have reserved privately for the two of us to go together?
I understand that I may just have to deal with separating from him to go to a female only bath. This wouldn’t kill me, I can probably do it, I would just like to know what options there might be in case I can’t handle going on my own. And obviously ones that won’t mind us having tattoos which I know also limits our options drastically.

We will be in Tokyo, Nagasaki, Fukuoka, Hita, Osaka, Kyoto

Thanks!

by ItsNotMeIPromise_