I had a very similar situation last year with my tenants' lease ending July 31, 2007. My tenants were trying to stay in my property indefinitely by asking me for all different lengths of lease extensions with different reasons for each. My tenants were awful (very deceitful) and I wanted them out, but they didn't want to move - sounds like the same deal with your tenants. If you're feeling generous give them a new contract for X amount of days, but do not give them any kind of lease extension. The reason is as follows:
If you decide to be "nice" to them and let them stay an additional 1 or 2 months past the lease-end date, in order to protect yourself from a lawsuit they will probably try to initiate in order to stay in your property longer, you need to let your current lease with them run out. Keep taking their monthly rent until July 31.
Then draw up another brand new contract (lease) with them on your terms. Since you want them gone make it a tough lease they won't want. You'll need a start date of August 1 and a definite ending date - whether that is for an additional 2 weeks, 2 months, etc. You need to state your new rent (see if your state will let you jack up the rent sky high - stay on the legal side of things - very high rent will discourage them from wanting to stay), and include any stipulations such as they will be paying for any repairs regardless of how they occurred, etc. Overall you want a tight lease in your favor - not theirs. You want to discourage them from staying on even one more day. If they don't like your terms, they don't have to sign the new contract, but then they do have to move on July 31.
They may come back to you and tell you that they don't want a new lease. Tell them that's all your offering, that you will not renegotiate or change the current lease in any way shape or form. That's legally how something like this is handled - anything else will end up with you being taken to court by them. As a landlord you have to protect yourself. This is the way to do it.
Whatever you do, don't change anything at all on the current signed lease - not even a comma. The minute you agree to change the lease for anything at all, your tenants will be able to initiate a court case that can drag on indefinitely, and you won't be able to get them out. Which is probably their goal.
The ultimate goal for you is to get them out.
Since my lawyer advised me that it would be in my best interest to get these people out (they really wanted to stay but they were awful tenants who caused me stress and trouble), what I personally did was to write them a letter (sent certified mail) saying something like "We expect you to honor the written lease which expires on July 31, 2008. Please leave the premises in clean and broom swept condition." At the bottom I put CC: my lawyer's name. That way they knew I meant business.
I don't believe you can start eviction until after the lease has expired assuming their rent is current - if your tenants are afraid of a bad credit rating they will move on time and not risk eviction. Be prepared for them to be anything but nice to you. My tenants were very angry they couldn't stay - that their ploy didn't work - they were outside in the front of my property having temper tantrums heaving bricks into the front lawn according to the neighbors.
All you have to do is hang in there for another 2 months and you'll be rid of them. I found myself not returning their pestering phone calls, etc.
Hope all goes well.