As scrubs stated "play what sounds right to you". Sometimes a song needs to resolve itself by means of finishing the song with the Tonic, however this can also produce the feeling that the song is going to carry on. Music has its theory but the rules are wide open. (Originality)
If the song sounds good finishing on the C chord, finish it on the C chord.
Sorry for not fully understanding your original post.
Light answered your question about modulation, which you did. However, on your original question, no you can't use C as the tonic of Am because A is the tonic.
It's typical to end minor key songs not only on the tonic, but also a major chord. But don't do that either, it also gets pretty boring.