Hey Mel,
first of all
to you for putting yourself out there. It's difficult and scary at the best of times, but with kidney disease also it's that much more daunting!
I think the 2nd or 3rd date is a good time to be honest. You need to be up front. The first date is never the time - you don't know if there's serious interest there or it's just a date, so no reason to bring it up, however you don't want to go too far down the track then tell him and have him think you were keeping secrets, which can then cause real trust issues. Besides, you don't want to get too far into something, and invest emotional energy, heart, then have him run for the hills because he can't handle the truth.
The hardest part, I think, is how you introduce the subject. Sometimes there is a natural opening - for example if he wants to see you on a day you have dialysis, and you need to explain why you're not available. However sometimes it's not so easy. Hopefully you can find a comfortable time or spot to just explain your situation to him. I don't envy that conversation; I've had to have it a number of times. Most times the other person(girl in my case) has been understanding and not run off, but it's just as hard as asking for the date to tell something like that and waiting for the reaction....
So anyway I think: do it sooner rather than later. If he doesn't want to deal then you haven't invested too much in it, and he hopefully won't feel like you've been hiding things or dishonest with him.
All the best!!