A set $A$ is Sidon if all pairwise sums of elements in $A$ are distinct. A pair of sets $A,B$ is co-Sidon if $|A+B| = |A||B|$, i.e., all sums $a+b$ are distinct with $a \in A$ and $b \in B$. We will focus on the setting $A,B \subset \{0,1\}^n$, where addition is coordinate-wise over the integers. We present a new general method that improves lower bounds on $|A||B|$ for a co-Sidon pair $A,B \subset \{0,1\}^n$. The binary co-Sidon problem is equivalent to a well-studied problem in information theory on uniquely decodable codes for binary adder channels. Our method improves lower bounds for the zero-error capacity of such channels, for any number of users.