Filehippo is an website in which you will find all types of softwares and applications. in this site you will not only latest version site but also old version softwares and applications from them you can download that software which suits you most.
Once I updated my google play services and after few minutes the phones gets hanged to much and I thought to un install the latest version and install again the old version but I dint kept backup of old version then I searched for old version of google play services. then starting only I saw old version of google play services in filegippo.com then I opened it and downloaded from there the old version of google play services so like filhippo helped me and from then I use this site as primary for search of old version sites and also check apps which are paid in play store my be free in this site and just say this site is use and I felt very helpful with this.