yeah you should have two images one is online and one is offline

if u have created your own images make sure that they have GIF format i dont think it work with other format

next do this

1st   give name    online. gif   to your online image that you want to add when its appear online

2nd  give name    offline. gif  to your offline image that you want to add when its appear offline

after that login into your hosting account   
go to file manger

then find   /public_html/hcl/icons        (hcl or anything that you have given name to your live support)   

in icon  folder you will see offline. gif and offline. gif images files (you can delete that or can replace or overwite while uplading your images)

now click upload and upload your both images  online. gif and offline. gif  that you have creted and given the same name as i have told above

hope this may fix your problem if not let me know