Digits Localization on Streets View House Numbersm
Since you are saying that you got box coordinates in the original image, why not reduce coordinates by exactly same scale.

For example a coordinate say $(100,100)$ in the image of say $(1024,1024)$ size when resized to say $(256,256)$ will be $(25,25)$ (assuming you didn't crop anything in the mean while), which is in general 

$$(x_{new},y_{new}) = (\frac{x_{old}*l_{new}}{l_{old}},\frac{y_{old}*b_{new}}{b_{old}})$$ where $l$ is the length of the image, $b$ is the width.

In times of fractional answers after reduction make sure your bounding box covers a bigger area. For example, Y-coordinate for the left side of bounding box should be pushed towards the Y-axis while on the right should be pushed towards the ceil value like say you got $25.5$ by reducing, go to 25 when on the left side while $26$ when on right side of bounding box. Similarly up and down for $x's$.

Hope this helps.