You would have to apply through an approved Swiss agency, being a non-EU national. Au pairs:
"The Law on Foreign Nationals, in force since 1 January 2008, has introduced the following changes:
Au pairs from third countries (e.g. USA, Canada, Thailand, etc.) can only receive permits if they are placed through an agency which is approved and licensed by the Swiss State Secretariat for Economic Affairs (SECO). Currently there are only few such agencies specialising in the placement of au pairs (e.g. profilia). However, we expect the number to increase throughout the year. Au pairs may now be placed only if they are between 18 to 25 years old.
Placement through an agency is not necessary if employing au pairs from EU/EFTA countries. The age range for au pairs from EU/EFTA countries remains between 17 and 30 years of age. Au pairs from "old" EU or EFTA member states (e.g. France,Spain, UK, Norway, etc.) receive their short-time residence permit or residence permit after presenting a work contract and registering themselves with the communal authorities. Au pairs from the new EU member states (e.g. Poland, Slovakia) still require a residence permit from the cantonal authorities."
Perfect Way is another agency to look at along with the Pro filia mentioned. http://www.perfectway.ch/en/for-fami...formation.html