Deleted iCloud contacts keep coming back

I had the same issue before. After some experiment, here is what I have found working:

Go to Setting > Mail,Contacts,Calendars > Fetch New Data > iCloud > Select "Push" (if you select "Fetch", the iPhone changes will supersede changes made on iCloud. It is up to individual preference)

After "Push" is selected, you may make all the changes you want to iCloud Contacts. Your iPhone will be updated in the next Sync.

Hope it works.

iCloud is a way to keep the same data accessible via all your Apple devices.

It isn't set-up to allow you to keep different data on different devices. If it were, then what would be the point of the service?

They're appearing in iCloud repeatedly because you have sync turned on.

However, you can disable just the syncing of contacts by going to Settings -> iCloud -> Switch Contacts to OFF.

Hope this helps!

These contacts are most probably stored not only in iCloud, but also on your device separately, in the device-only contact group called "on my iPhone".

Your situation is probably a remnant of the times when you synced the contacts via iTunes. Then they got migrated to iCloud and were effectively doubled, but you only saw one contact in the Contacts app, because your iPhone (or iPad) displayed only one entry when contacts were doubled like that.

What you need to do is go to the Contacts app, touch "groups" and turn off the iCloud group(s), but leave the group "on my iPhone". Then you will be able to ultimately delete the contacts that were there.