@Sarah Lewis
Several considerations. Just in case the decision wasn't hard enough for you.
If you refuse to extend, what makes you think they will pay at all? It would not be uncommon for tenants to decide that you are a jerk and that you can go &*%%^ yourself. They could probably find a homeowner friend who would act the part of a previous landlord, so they would not need your reference. They might even trash the place.
If they "find tenants" to take over the lease, it is meaningless. New tenants must meet your standards, not theirs.
I suspect that what amount of vacancy time is allowed varies by location to an extent, but I doubt if you would be allowed two months.
If you give them what they want, you are allowing them to manipulate you in a very bad way. Not a good way to deal with tenants. It sets a very bad precedent for future dealings with them and other tenants. I would accept all of the negative possibilities that go with refusing to re-sign, and pursue them for every bit you can get if they break the lease. Even if it costs you more than you get. Even if it means an uncollected judgement logged against their credit is all you get.
Get a reputation for being a hard-nosed but fair landlord, or tenants will dictate terms to you and you will lose. That is my two cents.