Check in/check out availability search

Hi there, I’m helping a friend build a vacation apartment rental site and can’t seem to find a plug in which can do a check in/check out availability search. Something like what you would find on a Hotel site to make reservations, like what they have on this site romanreference.com.

Is there such a plugin or way of modifying the search feature in WordPress to do this? If not, can someone recommend a free publishing software that would have such a feature? Any help would be appreciated, I’m stuck.

Thanks in advance.