Who is elder in Charlie and Alan?

Charlie is the older brother. There are jokes in a number of episodes that establish this.

Also, the Two and a Half Men wiki does confirm this:
Dr. Alan Jerome "Al" Harper, DC, is a character from the CBS sitcom Two and a Half Men. Portrayed by Jon Cryer, Alan is the hapless and helpless biological father of Jake Harper, roommate and best friend of Walden Schmidt and the surviving younger brother of Charlie Harper.

The wiki lists the years of birth: Charlie: 1967, Alan: 1969.