Address the invitation specifically to the child invited. Also, you could write a note inside to the effect of , "Please RSVP and let us know if Chris (child's friend name only) can attend" or "Hope Chris can help celebrate with us". I think you are better off being subtle, rather than directly stating it in the invitation, which may come off to some as a little crass. Anyone with reasonable sensibilities will be able to understand the meaning. If it is in question, then they can address it with you when they RSVP. When they call to RSVP, state, "Oh, I'm glad Chris can make it." If they then state or ask if the little sister can come too. Say she is more than welcome to come, but in order to accommodate all of your child's friends, you were, unfortunately due to budget constrictions, unable to pay for all the siblings of all the friends as well. Most parents would completely understand this. If they all show up to the event without telling you in the RSVP, say how wonderful it is to see them all, and I'm sorry I didn't realize you all were coming. We only paid for x amount of kids to participate, but if the other children would like to participate as well - they can buy some tickets over there.
Hope this helps and you guys have a wonderful celebration.