You can have only one keyboard active at the same time, so before opening a new keyboard check if the current one is done. A way to do it nicely would be something like (code written on the fly and I'm no javascript programmer so could be some small syntax errors in it):

var text1 : string;
var text2 : string;
var isTyping : boolean;

function OnGUI() {
    if (GUI.Button(Rect(10, 10, 200, 32), text1) && !isTyping) {
        StartCoroutine(COInputText1());
    }
    if (GUI.Button(Rect(10, 50, 200, 32), text2) && !isTyping) {
        StartCoroutine(COInputText2());
    }
}

function COInputText1() {
    isTyping = true;
    var keyboard : IphoneKeyboard;
    keyboard = IPhoneKeyboard.Open(text1);
    yield keyboard;
    text1 = keyboard.text;
    isTyping = false;
}

function COInputText2() {
    isTyping = true;
    var keyboard : IphoneKeyboard;
    keyboard = IPhoneKeyboard.Open(text2);
    yield keyboard;
    text2 = keyboard.text;
    isTyping = false;
}