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The Man in Seat 61 says that tickets can be booked on the online website of CFR, the Romanian Railway company. Here is the official CFR wesbsite. Quoting from The Man:
How to book trains within Romania
[...]
You can book Romanian domestic train tickets online at www.cfrcalatori.ro, the Romanian Railways (CFR) website, including domestic sleeper trains. It will only book the compulsory-reservation mainline trains, not local services, but it's easy enough to use and should have no problem with non-Romanian credit cards.