Actually you don't find christenings in the Bible anyway, it started in the 5/6th century. There is baptisms but only as an adult when you can make your own decision about things. There are baby dedications but that is a more informal affair with a couple of prayers, in our church done on a normal sunday morning service with the notices (takes about 10 mins).
Anyway, it's not a bad thing to do though, and a great celebration of a new life, no reason why anyone can't join in and read what they feel is appropriate.
If they've asked you to do a reading then they obviously feel like you'll be able to choose something nice.