First off I know in the book that Neri is responsible for Moe Greene’s death but in the film he is tasked with taking out Barzini. Given the fact that all the hits were carried out by trusted members who do you think took out Moe? I know that Pentangeli wasn’t created until after the first film but he would actually make sense given the fact that he was a trusted soldier and hated Hyman Roth. Although we know the hitman doesn’t look anything like Frankie since like I said he wasn’t created yet. My personal theory is that it was carried out by the Molinari Family. We know that they are aligned with the Corleones and they protected Fredo during the War. I’m interested to hear your theories!

The idea was abandoned, but in his planning notebook Coppola contemplated having Moe and his people greet Michael and Tom at the front of the hotel and escort them to their suite. The assassin would then turn out to be someone in Moe's entourage.

I am glad this planning was abandoned!
If I had not misunderstood, we would have missed out on, among others -

Fredo's welcome party! for Michael


Also I can't see Michael relying on the assassin to be someone in Moe's entourage
Michael undoubtedly would want the assassin to be from his own men

My speculation, for what it is worth!

Rocco linked to Michael
I doubt the Molinari Family even though aligned with the Corleones would carry out killings on the Corleones behalf
ie: guaranteeing Fredo's safety is one thing but....

If crime families start carrying out murder favours on behalf of other crime families when they have no direct personal beef with the targeted family, it gets too messy, bloodbath every corner and becomes disorganized! crime
Besides there is a Mafia code of conduct and honour....

Isn't that why they created Murder, Inc.? Estimates range from between 400 and 1000 contract murders.

I agree...too important to farm out, especially (in the movie) since it had to be precision-timed with all the other murders that day. I also don't think he would have had to use the Molinari Family, since Moe was not a made man in the Mafia. But, it raises an interesting question: The Molinari's guaranteed Fredo's safety--not from Moe, but from the NYC Families during the war. Their credibility was involved. Michael may have had to inform the Molinarri's of his plans to keep them on his side.

No doubt too important to farm out Michael undoubtedly would want the assassin to be from his own men

I don't reckon he would have used the Molinari Family
They guaranteed Fredo's safety not Moe's If Michael informed them then their appearing weak cover is blown

I agree it would have been someone from within the family, both due to overall trust as well as trusting the timing of the execution. I like the idea of it being Pentangeli. That would make all assassins other than Neri coming from Clemenza's caporegime. Quite a lot of trust was placed in that faction considering Clemenza was considered a risk to turn after Vito's death (not to mention initial suspicion for Vito's shooting as well).

I might add I can't see Michael asking the Molinari Family for murder favours - The Corleone pride like the Corleones can't handle their own hits....

Sure thing it would always be "someone from within the family" even if a civilian!
Remember! civilian Michael was sent to kill Sollozzo and Police Captain McCluskey

In fairness, everyone except Tom [even so Tom was seemingly still kept in the dark of Vito and Michael's Baptism murder plans] “was considered a risk to turn after Vito's death” until Tessio outed himself as the traitor

Clemenza has to answer for Paulie since Paulie was a member of Clemenza's regime and no clearance for Clemenza until establishing Paulie was acting on his own “for Vito's shooting”