This Wikipedia article seems to suggest that NASA no longer owns an aircraft capable of simulating weightlessness, and that such astronaut training is now contracted from a private company. Can this be confirmed by an independent source?
The last NASA reduced gravity aircraft I can find is a C-9, registration N932NA, which is listed as stored (i.e. mothballed at Davis Monthan).
This agrees with the note on the Reduced gravity program page:
Website updated September 29, 2014
NASA has not decided how or if Microgravity Flights will occur in the future. This website will be updated as new guidance is released.