Reporting IRA conversion that happened after Jan 1st.

Hi, 

I'm wondering if it's possible to report Traditional to Roth conversion for year X if the conversion happened in year X+1 before the deadline? My understanding is that I will only receive a 1099-R if the conversion is done before the end of year X. Given that I did the conversion for the tax year X but in year X+1: 

1) Should I report that in year X or X+1?

2) Would I be able to do another conversion for the tax year X+1? 

 

Thanks,