From the Jerusalem Post:

Visitors no longer have to hold cardboard kippot on their heads when visiting the Kotel: The Western Wall Heritage Foundation has received a donation of 1 million nylon yarmulkes.
According to a statement Wednesday from the office of the rabbi of the Western Wall and Holy Sites, the distinct and sometimes awkward cardboard head coverings that have been offered to male visitors to the site for 40 years have been replaced.
The white cloth yarmulkes, which were apparently made in China to cut costs, were given to the foundation on Sunday and are now available for use at the entrance to the Kotel area.
Though this is not the first time new yarmulkes have been donated to the Kotel, said the rabbi’s assistant on Wednesday, this is the first time there has been a large enough number to accommodate the more than eight million people who visit the site each year.
[. . .]
The new yarmulkes, like the cardboard ones, are considered “disposable” – people are allowed to take them home. But the old ones may become a collector’s item: Some are being sold on ebay for $6.

The full story is here. You can buy a cardboard kippah on ebay here.  If you’re wondering why it’s sometimes called a kippah and why sometimes yarmulke or even what one is and why they’re so important, this Wikipedia article has some good information.