"Please promote to our contributors the electronic journal" - This sentence is understandable but the words aren't arranged clearly.
"Please promote our contributors the electronic journal" - This sentence isn't properly formed and it isn't understandable because you don't link the verb (promote) with the noun (journal) with a word like "to". Also, the words aren't arranged clearly. To make it understandable I would write...
"Please promote the electronic journal to our contributors".
What do you want to do? "Please promote"
What do you want to promote? "the electronic journal"
Who do you want to promote it to? "to our contributors"