Cheap and twin in almost the same sentence.
It will depend to a very large extent on the number of hours you're going to fly in that month. Twins available for regular self-fly rent are typically workhorses for a school and can normally not be missed for an extended time. Plus they will have a minimum hours requirement on them if you take them for an extended period. If you are going to meet that minimum requirement it'll still be rather expensive.
On the other hand, there are twins in hands of private owners. If you are able to strike a deal with them, particularly if you're not leaving the local area so that the owner can use the plane if he/she needs it, you might get almost unlimited use for a reasonable price.
So we really need to know what you intend to do with it before we can give you better advise.