Nothing would satisfy that boy but that I place him on my lap.

but that在本句中相当于if…not作“若不; 要不是;除非”解，本句前部分是虚拟语气，后面表后面表事实。再例：

I would go abroad but that I am poor. 要不是我穷的话，我就要出国了

I would have failed but that your helped me.要不是你们帮助我，我就会失败