There won't be new kanji for the elements in Japanese.
For Chinese, however, there's a call on naming (and writing) the new elements by the China National Committee for Terms in Sciences and Technologies.
From the Babelfish:
( 1) According to the principle of creating new words as little as
possible, Make the word, try to use the existing ancient word.
( 2 )
selection or new Chinese characters should be in line with national
( 3 ) to meet the shape of the characters as the main
character writing features to reflect the nature of the element,
pronunciation close to the international naming.
( 4 )
to avoid the
same name with the previous elements, to avoid the use of polyphonic.
( 5 ) the use of simplified characters, to avoid using weird words, use
less strokes of the word.
( 6 ) In order to avoid ambiguity, word
selection should try to avoid the life of common words and has been
used as other industry-specific Chinese characters.
( 7 ) as far as
possible the use of simple and uncompromising words, in order to
facilitate the cross-strait and the Chinese circle of scientific and
technical terms of unity.
Taiwan may or may not find their own names and characters.