Great post from Italiangreyhound
Just you sound like a lovely supportive partner but honestly, your partner sounds like a total waste of space... sorry, but really...
What on earth would he do without you? He earns about £20 a month or whatever, how would he cope? I think you are enabling him to be like this, I honestly do. Sometimes when people leave Uni, they just pratt around trying to find their way and trying different things to see what they like, and faffing around whilst others pick up the pieces, and your partner sounds like one of these. You (and he I presume) are putting a lot of faith into the counselling possibilities but is it a bit pie in the sky? If all you have both done is chat to a couple of people you know who said it would be good, that is hardly formal research into earning potential is it... ?
I know someone who has done similar. He combined his studies with some voluntary work and some care work, he is three years down the line and he has two clients who he counsels, so far it's only pin money and he is much older than your partner and it is a career change for him after enough redundancy money to cushion this choice. It can take years to build up a counselling business.
He needs to get a job that fits in round his studies and I know you say there aren't any, but he must start with looking close to home and if there isn't anything, he should extend his search further out bit by bit. There are jobs out there if you get your head down and really really work on it. Get him to do a flyer (it will have to be worded in such a way that makes him ready willing and able to take on anything), and he should take them round shops/pubs/businesses and sell himself.
How long does your partner spend online (not gaming!) looking for work? There is possibilities out there but looking for a job has to almost become a full time job in itself. Your partner sounds rather passive and lazy to be honest and the longer this goes on the more frustrated you are going to get because you sound like the driving force in the relationship.