My tenant notified me today that she and her husband are divorcing. They are both on the lease which has about 7.5 months left on it. The list lists them as jointly and severally liable. I believe I have no legal obligation to break the lease for this reason, but I don't want to force a tenant to stay in a situation if it's a financial difficulty. If she's going to struggle to pay, then it seems like it's in my best interest to ensure a smooth transition. 

I have offerred to let them out of their lease if they or I find a qualified tenant to replace them. 

Any other suggestions on how to approach this? 

You have no obligation to let them break the lease but at the same time they can just split on you and other than any deposit you have it may be difficult to collect beyond that despite what you are owed.  Your best options are to work with them and find a new tenant and let them out once a new tenant is located and that lease begins or to negotiate a lease termination fee releasing them from the lease (such as 1-2 months rent).   If they don't have the money to stay or pay the lease break fee what benefit is there to you of trying to hold them to lease?  You're going to end up either having to evict or having them split on you if they can't afford it.  

My parents had this happen to them twice.  In the end they let the people out of the lease because it is better to have a smooth transition out than end up with late rents and things spiraling down.  Tell them if they leave the place clean and ready to move in you will give them a good reference on their next place and wish them well.  Work out something where you can show the house to potential tenants while they are still there by appointment especially if there isn't anything major that needs to be done to the place.  If you have any smaller less expensive units you can move them into soon see if you can work a deal there.

Don't give away any of your rights in the lease, even verbally.

Make sure they know that anyone they find to take the lease will need to be acceptable to you.

Ask them to keep the place looking good so that you can show it.  List it and try to find new tenants.  With any luck, you can find new tenants with 0 days vacancy.  While you're at it, initially try listing it with a 5% boost in rent.

Couple of comments I'd add.

1) Do they want out of the lease? If so, thats a good thing. It means you should be able to get them out without an eviction. 

2) I'm assuming they paid this month's rent already. If not, start the eviction process (i.e. 5 day notice, etc)

3) I'd offer that if they are out by the first of the month, you won't come after them for breaking the lease.  I understand Raj's suggestion that you shouldn't give away your lease rights. But bottom line is you need to give them some incentive to get out.  

But let them know you will have to keep their security deposit and that you will be listing the house immediately and doing some showings a couple of agreed upon times/days.

As long as you're keeping their security deposit, that basically gives you an extra month to find someone and still not take a hit on the vacancy. And, while I know that isn't always easy this time of year, the bottom line is thats not too bad a deal given the situation.

The key thing you want to try to avoid is the eviction. And be sure to let them know that they're going to want to avoid an eviction as well as its going to make it extremely difficult for them to find a new place if they have evictions on their record.....

I've had it work out well for me the last two times in terms of getting them out.
1) Bradley house - had a young couple that was engaged. Broke up. They were so afraid of breaking the lease and getting hit with a big chunk of money that they moved out mid month and let me keep the deposit as the fee for breaking the lese. I got a new tenant in by the first and essentially was able to double dip on the rent for a month.

2) Bourb house - had a married couple that split up. Wife had moved out and she was making the money. Husband wouldn't go. Threatened the eviction and that got him out. But he was really dragging his feet. Claimed he couldn't get anybody to help him clean the stuff out. I told him to leave it and just get out.

Cost me some money to clean the place out and replace some carpeting in the back room (I replaced with laminate). But still, the threat of eviction helped get them out at least.

And aside from the cleanout and laminate, I was able to get it rented right away. Security deposit covered some of the loss so I basically only ate about a month or so of vacancy in cost. Not bad considering thats about what I have for a typical move out anyway.