Kagoshima-Chuo to Beppu Station

We are planning to move from Kagoshima to Beppu station on 24th Feb Monday. Checking the train and shinkansen timing, we need to travel down all the way to Kokura station and change to a limited express train to Beppu, it travel long distance & take long time.
We wish to know is there any local train whcih able to connect between Kagoshima - Kumamoto - Beppu....?
Thank you

[Rail map]
http://www.jrkyushu.co.jp/english/time_table/time_table.html
Take via Miayazaki,Nobeoka(east side) route by LtdExp(Not Shinkansen) Kirishima and Nichirin.

or if enough time until Kumamoto by Shinkansen
then across to Oita(Beppu) by Kumagawa or Aso boy.
or until Kurume by Shinkansen
then take by Yufu in no mori not so bad.

http://www.hyperdia.com/en/