The correct way is (be)(ing). The contraction for be should be used (besides when it is standing alone!) when it appears at the beginning of a word and makes up the first syllable. It’s called a lower groupsign (UEB 10.6). It must also be followed by a letter, contraction or modified letter in order to use the contraction.
In words like being, begin, beware, the letters be make up the first syllable so the contraction should be used. In words like benediction, beneficial, beat, bedspread, the letters be do NOT make up the first syllable (ben-, beat, bed-) so the contraction for be cannot be used.