Are there any relatively cheap laptops that can run minecraft at 60+ fps?

Absolutely! The minimum required to run Minecraft effectively at 60FPS is Aim for Windows 7 64bit, (AT LEAST) 4g DDR3 RAM, a dual-core or quad-core processor, and of course a large hard drive for your files. Looking at Asus computers, you should be able to get a reliable laptop that will work for $250-$300.