Having a dreadful time with my housemate who is always going on about his Ex and not seeing his kids and the Family Court. I know it must be rough for him and I don't fully understand how bad it is for him, but I am getting a bit tired of hearing about all this negativity. Do I tell him so and possibly risk our friendship and conflict or do I find another place to live?

A toughy alright. If you have the patience and headspace you could validate his pain before attempting to alter his perception. ie. giving him continual yet periodic doses of a brighter side of life and what he can be grateful for.

Or tell it to him straight about how you feel and what you think. If he respects you at all he may take it on board and help him make some internal changes.

However, if he is in a fragile state you may want to to tread carefully.

Or else as you say, move.

Change can take along time and alot of effort by the person in question. It's a choice for you Wayne about what you can and want to do.

Firstly Wayne, in order to really be supportive of your housemate/his terrible situation you need to work towards understanding how bad it is for him. So I suggest to have a heart to heart or speak openly & compassionately with him about it. Let him, allow him to express his frustration about his Ex & not seeing his children & the family court.

This is very tough, heartbreaking on people who experience this life changing & traumatic, stressful situation.
You could also start educating yourself further on understanding the grief, trauma & loss people; including your friend experience when going through situations he's in/experienced.

But it is unfair to take on a tired of hearing attitude about his negativity without trying to fully understand or not fully understanding it. Have compassion either way & when he keeps going on as you say, try a different tactic, like delving deeper into why he is needing to obviously talk about { & with you } his ex, not seeing his children which is heart breaking for anyone who cares about their own children, wants to be with them & the tough, merry go round family court situation.

Maybe he is needing to vent with you as his friend, housemate you can help each other & learn from this experience too.
Maybe he has no-one else he can vent as much with. If one is to be a true friend then they need to have more patience, reach more understanding & compassion for their fellow friends & humans when they are going through or have gone through very rough times, trauma, grief, loss & heart ache of not being able to see their children, financial loss & the list goes on. So for yours & his sake try to reach a more understanding attitude & give opportunities for yourselves to talk about your mates issues, delving deeper as need be so you can have better opportunity to understand how he feels, why he vents as you say & his whole life situation as mentioned.

And maybe this will even bring your friendship closer, better understanding & better living circumstances, easing the tension. Cause it would be a shame if you simply moved out, leaving your friend desserted & issues between yourselves unresolved. Also dis-rupting both your lives further.

I can understand why even without knowing either of you why your friend needs to talk about his troubles, worries with his ex, not seeing his kids & the family court.

And I too am in similar situation only my child is in my care, lives with myself she is a great, beautiful, loving fur child { puppy dog }.
My ex partner chose to separate, dessert me after 18.5 years or so of marriage for non-justifiable reasons as many people leave their partners, separate & divorce etc.