Looking on the internet deeply has found these results:

Eyes beaming with happiness is the most popular phrase on the web.

Eyes beaming with exuberance 10 results on the web	Eyes beaming with happiness 118 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Jul 27, 2015 ... What a joy to look into eyes beaming with happiness when we had unwrapped all the packages! The children would have loved to try the new ... He could not supply the word she had meant; but in her charming eyes, beaming with happiness, he saw all he needed to know. And he wrote three letters. He could not supply the words she had meant; but in her charming eyes, beaming with happiness, he saw all he needed to know. And he wrote three letters. Jan 28, 2011 ... ... been playing, and said, his great eyes beaming with happiness, “I do not wonder that Christ said, of such as these is the Kingdom of Heaven!

Eyes beaming with exuberance

10 results on the web

Eyes beaming with happiness

118 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Jul 27, 2015 ... What a joy to look into eyes beaming with happiness when we had unwrapped all the packages! The children would have loved to try the new ...
He could not supply the word she had meant; but in her charming eyes, beaming with happiness, he saw all he needed to know. And he wrote three letters.
He could not supply the words she had meant; but in her charming eyes, beaming with happiness, he saw all he needed to know. And he wrote three letters.
Jan 28, 2011 ... ... been playing, and said, his great eyes beaming with happiness, “I do not wonder that Christ said, of such as these is the Kingdom of Heaven!