I did them at the same time (day and night), DS is dry day and night now (I think he'd still be wet at night if we had a nappy IYKWIM). I'd suggest just putting a mattress protector on and taking the nappy off. Don't put undies on him at night (they can feel like a nappy) and tell him he needs to go to the toilet overnight and first thing in the morning. Might be worth using a baby monitor so you can hear when he wakes and take him straight to the toilet.

Good luck!