Feed script variable to command that prompts for user input

If pushcommand simply reads first username and then password from standard input, separated by newline, you can do the following:

echo "$usernamen$password" | pushcommand

The "echo" call here will output the username and password variables on separate lines.
The "|" means "take the output of the command on the left, and feed it as input to the command on the right". This construct is called a "pipe" in shell scripts.

For scripting more complex interactions, I'd recommend looking at expect or possibly kermit. To get help with expect or kermit, you'd have to post an example on how an interactive use of pushcommand actually looks like, e.g. what prompts it displays and so on.