Of course there can be and there is. You will see if you look around you that there are many good, decent, kind, and downright cheerful people that don't believe in any god. You may use labels for them like secular, atheist, or just godless, but you would be surprised if you got to know them. They are not hopeless people. They do not fear god. They do not believe in god.
However, the vast majority of these people are good, honest, and have a strong moral fiber just like many god fearing people. Having faith in god doesn't make one more moral. Either you have it or you don't. People capable of horrible things don't discriminate. There are just as many god fearing criminals as criminals who do not believe.
The simple answer is, Yes, there absolutely can be morality in a society without god. I don't believe our society will ever become completely devoid of god fearing people, but remember it's okay to believe, nor not believe, and if you don't believe you can still be a person with strong morality.
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