If I understand you correctly, you are looking to contribute (not convert) money to a Roth IRA using assets currently in a taxable account. You would be restricted by the contribution limits and the earned income restrictions. As I understand it, you would be taxed on the gains of the assets sold from your taxable account, since all of your Roth contributions need to be post-tax.
However, if you have specific holdings in that taxable account that have not appreciated, you might be able to sell those assets without incurring taxable gains.
I wouldn't take my word for it though...