It's been a long time since we needed a diaper bag, but he was OK with packing it. To help both of us from forgetting the essentials, especially when we went her to daycare, I attached a small luggage tag with a list of the contents.
I also leave ours packed all the time, so all DH has to do is grab it. He often doesn't remember to do that It happens often that I take the baby down to the car, DH plops into the driver's seat, and I say "diaper bag?"
In 4 months I don't think he's ever done it from beginning to end. We CD so I try and make sure there are always diapers, a wet bag and wipes in there, plus a spare outfit. He might throw a blanket in, but always asks me if there is anything else.