I came up with this one myself:
When you see me you smile,
I only stay a while,
think outside the box my friend,
until you bring me to my end.
Where did my buddy go?
Their name had the sound of low.
Who am I, and who is my buddy?
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a nicely wrapped PRESENT?
When you see me you smile,
Receiving a present generally makes a person happy and puts a smile on their face.
I only stay a while,
But the present itself has only a temporary existence - it will soon be unwrapped to reveal what it truly is.
Furthermore (thanks to @QuantumTwinkie in comments), 'the present' (as in 'the here and now') only lasts a moment before it becomes 'the past' and part of history...
think outside the box my friend,
until you bring me to my end.
Until you open the present ('bring me to my end') you do not know what is inside the wrapped box. You can speculate about its contents, but you are quite literally thinking outside the box all the while it remains wrapped up.
Where did my buddy go?
Their name had the sound of low.
Once the paper and other wrapping materials are removed, they are taken away. Your 'buddy' who has now gone is a decorative BOW (which rhymes with 'low').
You could be
a bullet
Your buddy could be
a Submachine gun
When you see me you smile,
Looking at your reflection near the end of the bullets tip, your mouth may appear to be smiling due to the distorting curve.
I only stay a while,
The bullet only stays still for a while until fired.
think outside the box my friend,
Bullets are kept in boxes.
until you bring me to my end.
Bullets are spent/fired by striking their ends.
Where did my buddy go?
The bullet was fired and no longer with its buddy, the gun.
Their name had the sound of low.
Had trouble finding things that reference to low, so - SUB - machine gun or SMG.
If you are inspired by William Wordsworth for writing poems it could be:
Rainbow and the Sun
because
We smile when we see it... it never comes alone... it only stays till his buddy is there... but sadly or happily we can't end it...