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.