Why don't you ask him to take your luggage to the second floor?
Maybe you could ask him to carry your bags upstairs.
使役動詞 have や get を使って言うこともできますが、少し上から目線な言い方に取られなくもないので、私なら ask を使って言います。
ーWhy don't you ask him to take your luggage to the second floor?
「彼に2階まで荷物を持って行ってもらったら?」
Why don't you ask him to ...? で「彼に…してもらうようお願いしたら?」
ーMaybe you could ask him to carry your bags upstairs.
「できれば彼に2階まで鞄を運んでもらったら?」
Maybe you could ask him to ... で「できれば彼に…してもらうようお願いしたら」
ご参考まで!