There are lots of ways to get props other than musicals, such as in the building in Opelucid City with the guy handing out Props each day (four times), or, there's another lady in the same building who says how many Props exist. Once you know the amount, count your current Props and see how many you are missing.
You may not have this Prop either;
On your birthday (relying on DS), talk to the guy on the second level in the musivcal building and he will give you a Birthday Cake.
This guy also hands out Props on other occasions or after a musical, so check him from time to time.
EDIT:
If you place in the standings a rank that you don't usually get such as 4th effect the props you get; you can get them all by living of getting 1st all the time, for example.
