I agree that the tone is playful but paradoxically so. The lights the fireflies and the stars emit are symbolic of their life span and/or their vibrancy. One on hand, by comparison, the fireflies do not live very long at all. They can only attempt to simulate the relative immortality of the stars. They cannot sustain it: they die. This is a melancholy tone on how fleeting life is. On the other hand, the playful tone seems to celebrate the stars’ audacity at attempting to imitate stars. So, the poem is both melancholy and optimistic. This characteristic of ambiguity occurs in more of Frost’s poetry. For example, in “The Road Not Taken,” the speaker bemoans the anxiety of making the wrong choice but celebrates the ability to choose.
This is a lovely short poem by Robert Frost, reflecting his love of nature and the natural world, which are, of course, key elements in so many of his poems. This poem concerns the way that fireflies are able to "emulate" the beauty of the stars at night and achieve a fleeting similarity. Note how Robert Frost seems to employ a playful tone in this poem, punning on the similarity of "start" to "star" and ending with a rhyming couplet that is humorous and light-hearted, whilst also making the serious comparison of the light that fireflies emit and the celestial light that the stars provide us with:
Achieve at times a very star-like start.
Only, of course, they can't sustain the part.
Such an approach to comparing stars and fireflies seems to show the whimsical, playful tone that is at the heart of this excellent poem. It displays affection for fireflies whilst at the same time commenting humorously on how they only emulate stars partially.