Trawl round all the shops who have people delivering. If they don't have anything at the moment, look desperate and ask them if they would put you on a waiting list because you are really keen. Ask if you could be considered as "cover" should a regular not be able to do it.
While it's great to have the extra pocket money, it can be a bit of tie sometimes when other exciting things are on offer. Can I recommend that you rope in a friend who would be willing to cover for you when you are maybe sick or have something else more interesting occasionally. Show them the "round" a couple of times.
Let your employer know that you can provide sickness cover should you have a bad cold or similar, which, hopefully will impress.