Greetings, Rob, and welcome. You asked:
<<Can you open the account and make a 1999 contribution but not make a 2000 contrib (until after April 14)?>>

Yes, you have until April 17, 2000, to make a contribution to an IRA for tax-year 1999.

<<Also, Is there such a thing as a joint Roth IRA or do you need to set up two: His and Hers?>>

You need to establish two. An IRA cannot be owned jointly with someone else. That's why the "I" in IRA stands for Individual. :-)

Regards..Pixy