When Michael, before meeting with Moe, hit up Johnny Fontaine to agree to sign a contract to appear at the Corleone run casinos five times a year, it seemed Johnny wasn’t too happy about that. Maybe appearing that many times a year would eat into his movie career. Of course his hands were tied and like he said, “I’d do anything for my godfather.” But he didn’t seem to be a happy camper about it. Am I wrong?

Could be, Geekboy. I didn't see any overt unhappiness in Johnny. But I was always struck by his saying, "I'd do anything for my Godfather," and not, "I'd do anything for you (emphasis added). In the novel, in an earlier setting, Tom visits Johnny in Hollywood to tell him that Vito will help him get an Oscar, and will help arrange financing for a movie Johnny wants to produce. Johnny asks if he'll have to do favors in return, and Tom says of course he will. "The Godfather has to ask me himself," Johnny replies. "I won't do it if you or Sonny ask.".

I think that particular moment might be a vestige of what's in the book. When Michael mentions recruiting others to perform, Johnny's doubtful, but then turns around when Mike hints Johnny can spread around some points in the hotels to get it done.

I totally agree with your observation Geekboy.
Johnny's body language and overall tone seems to suggest that he was thinking "I'm never going to get out from under the Corleone's thumb,so best to just go along".
Even though it made his career,I bet there were times that Johnny wishes he would never have gone to Vito in the first place.

IMHO,when Johnny said that to Tom,he was doing it more to prop up his self-perceived sense of ego by suggesting that he would only answer to Vito.
In reality,after seeing first hand what the Family was capable of (the bandleader, Woltz,etc) Johnny had to know that he was nothing more than a common minstrel,bought,paid for,and owned by the Corleone's.
I would love to hear him refuse a favor that Tom asked . "No problem Johnny,if you don't want to do it,fine.I gotta get back to New York now.I promised your Godfather I'd keep him informed. What's that? You changed your mind? Ahh Johnny that is most appreciated.I see why he loves you so much"

No doubt Fontane knew everything he was, he owed the Corleones and always in their debt, forever

I reckon there was confusion than unhappiness because no one knew the Don is semi-retired and Mike is in charge of the Family business now and that his Godfather is now Mike!

If I remember correctly, Tom was impressed by this, and by other comments made by Johnny. He flew into Hollywood thinking Johnny was a flake, but flew out with a new appreciation for why Vito thought so much of him.

Your memory is right, Luca. Also, at Connie's wedding, Tom has a twinge of jealousy over Vito's concern for Johnny.

Johnny Fontane was pretty much a nobody without the Corleones

Vito Slapping Fontane in the face - Extracts:

Tom was right!
and he [Fontane] was!