Since I've been reading some books and fanfictions written by people whose Italian is not their first lenguage (or they don't speak it), I felt like giving some tips as native speaker for writing pet names/nicknames for love stories when you write one.
This is very common when you're writing about enemies teasing each other or just someone being cheesy and flirty.
Cucciola/Cucciolo: (cute puppy)
This is VERY confidential. In Italy we call a person this when they do or say something that's unbelievably cute for them or it's classified as "vulnerable". I reccomand to use it with long-term relationships.
Amore/Amore mio (love/my love)
Patata/Patato (cutie patootie)
This is maybe the most famous, but we use it even between family members, for example, a mother calls her son "Amore" when they're saying goodbye ("ciao amore, buona giornata").
This is very common among couples. The shortened version, "Teso", is more used among female bestfriends.
This is used a lot to call someone "cute", even between friends, mostly used to the elders to call some antics their younger teammate/partner/friend etc. does.
This is almost unused now, since it sounds very "800s". Though if you want to use, just know it's VERY flirty, like high levels.
Alternative for Dolcezza. This sounds "cuter" to use.
Mia cara/Mio caro (my dear)
Can be used even without the possessive pronoun (mia/mio), sounds better without them. Can be used even in non-romantic topics, perfect, for example, to be used in platonic relationships, mocking and sarcastic jokes or just bossing around.
An alternative to Patata/Patato.
This is very common between female besties. They call eachother like this instead of their names very often.
Alternative to "vita". This is more confidential.
Fra/Fraté/Compà (dude/bro)
This is used between male bestfriends but it's not rare that even girls use it to call a person of any gender.
Hope this helped a little from the same basic and usual stuff. If you want other categories just ask in the comments or send a request! (gladly accepted)