I live in Tennessee and I am renting a place and I have no lease agreement I got behind on my rent but am still paying can they kick me out in thirty days with small children?

The fact that you have small children isn't a defense to an action for eviction, if that's what you are asking.

Yes, the number of children does not matter. Here is the eviction process in TN: "If you are renting on a month-to-month basis, you may cancel the lease by giving the tenant 30 days' notice. The 30 days begins to run after the rent is due for the next month after the tenant receives the notice. For instance, suppose that rent is due on the first of the month, and you give the tenant notice to leave on March 10. The next rent payment is due on April 1, so the 30 days' notice begins to run on April 1; and the tenant does not have to leave until May 1."

The details are here - Tennessee Evictions (http://www.rentlaw.com/eviction/tenneviction.htm)

You can be evicted for late payment of rent or simply because the landlord doesn't want you there any longer.