He's allowed to stay as a guest for 3 nights a week, without it effecting you. Would be a good idea to let social welfare know about this. If they find out from another source and dont get the correct information then it could cause trouble for you.
Is he working at the moment? And is he paying you maintenance? Even if he isn't working he would need to be giving you something even if it is only 10/20 euro a week.
Remember he is a guest, the first proof they get that he is more than that you will lose your benefits, and it's tough to get them back. I know he is your partner and your childs father but for staying over you cant think of him that way. i.e he wouldn't have a huge amount of personal items there, he does have another address, no bills are registered to your address ect ect