When is the cherry tree the loveliest according to "Loveliest of Trees, the Cherry Now"?
The poem does not actually say the cherry tree is lovelier in one season than in another. It says it is the loveliest "of trees," that is, lovelier than the other trees. However, the poem is clearly about the cherry tree in spring.
Other than the obvious fact that trees bloom in the Springtime, two other lines in the poem show us that the poet is contemplating the cherry in spring.
The cherry tree is said to be "wearing white for Eastertide." Easter comes in the spring.
The poem actually mentions spring:
And since, to look at things in bloom,/Fifty Springs are little room...
Since trees only bloom for a brief period during the spring, each year's blooming time is precious and fleeting. The poet is counting how many more times he will get to enjoy looking at trees (particularly the cherry) blooming before he dies. He estimates that he has "fifty Springs" left, which does not seem like very much time to him.
Whether the cherry tree is actually loveliest in spring is a matter of opinion and a bit hard to judge. It's like being asked to choose your favorite season. However, no one can deny that after a long winter, a tree blooming in the spring is a glorious, uplifting sight.