100 milliamp coil current...transistor or MOSFET?

Why dose every one think that a Atmega 328p can source and sink 40 mA the datasheet said that's not going to happen the chips VCC and Gnd pins can only source and sink 200 mA now there 23 I/O on that chip do the math 23 times 40

You are miss reading things. This is a limit you should not exceed, it is not a limit that can not be exceeded. It is perfectly possible to exceed these limits only you should not if you want to avoid damage to the chip.