Are there any reasonable grounds for supposing that whatever the gods do is moral even when what they do would be immoral for humans to do?
For instance, can a deity like Zeus rape a woman and it be moral for some reason? If so, what is that reason?
Or, if you believe it would be immoral of you to sentence someone to be eternally tortured for failing to believe in something indemonstrable, such as that there exists an undetectable leprechaun farting invisible rainbows on the National Mall in Washington, would it still be moral for a deity to sentence someone to the same punishment for the same offense? If so, why? If not, why not?
Simply because someone is bigger and stronger than you doesn't make them right, the same applies to many gods. The Greek gods were imperfect in this way with their own emotions and lusts, they would fight and punish each other too, they were like us but with a lot more power in their hands.
I would say that with my God as well, (the Christian one), simply because He is mighty and powerful does not make Him always right, that isn't what defines His goodness. I do believe He is always right, for clarification, but not because He is big and immensely powerful.
In fact, even when God gave the Israelites the Ten Commandments, he didn't expect them to just accept it because "I am God I'm right these are your rules", the first thing He tells them before giving the commandments is "I am the LORD thy God, which have brought thee out of the land of Egypt, out of the house of bondage." God proved to the Israelites who He was, a Saviour who truly cared about them and liberated them from slavery.
God proves His character to His Creation, that's why I can trust that my God is moral, the highest and most infinite good. Often when it talks about God "seeking His glory" in the Bible, this is what it's all about, demonstrating God's character, His being to His Creation and His attributes shining throughout it. He hardened Pharaoh's heart to demonstrate His power and authority, He would often save Israel for His own sake, He would give up Israel to wrath too, for His own sake. And finally, in the ultimate display of God's holiness, humility, love and grace, the glory of God shone out as Jesus died on the cross for us, the hands that flung the stars into space were nailed to a wooden cross, for us.
That is why I trust God is good, because what He has done for me, through the person of Jesus Christ and throughout all of history.