Styleable html combobox?

I want to have a combo box with a drop down that shows suggestions from a list of options, as the user is typing. I have done it with this code:

<input 
    id="TagAddBox" 
    type="text" 
    list=TagAddList
    placeholder="+ New Tag"
    oninput="myFunction()">

</input>
<datalist id="TagAddList">
    <option value="Apple"></option> 
    <option value="Orange"></option> 
    <option value="Peach"></option>
</datalist>

My problem is, I can't style the stupid datalist because that's just the way it works. Boy, I just love front-end development with those gazillion stupid bugs and limitations and support issues that are everywhere.

So, I might need to implement my own drop down list from scratch, it might seem. Surely anyone must've done that before?