First thing's first - you can't record the additional income through PAYEanytime (self employed income is not Schedule E).
Next issue is what IS the correct way for you to return the income.
If you intend to make more than €3,174 of taxable income from your part-time business then you should register for Income tax self assessment using a form TR1. You will then be able to register for ROS (as it will then recognise your tax ref as an ID), and pay & file online.
If you are on a very small scale and not likely to exceed 3,174 of taxable income then you do not need to register for income tax, but you'll have to submit a paper Form 12 tax return after the year end, as PAYEanytime isn't set up to cater for that type of income.