Can I get a D train from Beijing to Chengdu East Railway Station?

I'm afraid not. The only four trains run between the two places are all not D trains.
You can try to fly to reach Chengdu or take the common trains.
The four trains will arrive in Chengdu in the morning or noon time, so your traveling plans may not be effected by the train schedule.

Thanks for your help. I will take a K train I think.