I am a PAYE employee and I have some rental income also that I will declare on my Form 12 (the net extra income amounts to less than €3174, so Form 12 is the correct one AFAIK). I understand that usually the income is coded against my tax credits, ie my credits for next year will be reduced. Is it possible to pay what I owe by cheque instead when sending in the form and leave the tax credits unaffected?
Yes. Register for Income Tax using a TR1. This way you complete an annual Form 11 due for filing and payment by 31 Oct following the calender year in question.