あまり高くない二人部屋を予約したいのですが。

English Translation

I would like a less expensive double room.

This original Japanese sentence has two problems.

First, 二人部屋 includes both a room with two beds (= ツインルーム), and a room with one large bed for two (= ダブルルーム). ツイン and ダブル are common terms in the hospitality industry. You need to specify which one you want to make a reservation.

Second, あまり高くない部屋 means “affordable room”. The English sentence with “a less expensive room” suggests that the couple was first recommended a more expensive one (e.g. 2K dollar per night), and they want a lower pricing (e.g. 1K per night). But they are not necessarily requesting an “affordable” one (e.g. 100 dollar per night).
My alternative translation is:

もう少し安価なダブルルームを予約したいのですが。(もうすこしあんかな…)