My daughter was born Oct. 6th and will probably not have a Social Security Number before the start of the new year. Is there a way to contribute to a Roth IRA in her name without her SS #?

You need to get a SSN because you will need that for your tax returns in the coming years, and the process may often start right at the hospital if they provide the forms.

With regards to a Roth, an infant is very unlikely to have "earned income" for a Roth IRA. However, you can start an educational IRA for the child with a max annual contribution of $500.

What might qualify as "earned income" for a infant? The only thing that comes to mind is modeling income ala Gerber ads... and that is a stretch. As the child gets older, you might see income related to babysitting, newspaper delivery, lawn mowing, etc. that might support a Roth IRA.