You can walk next door to the Blue Tang Inn. They rent bikes for $10 per day. Talk to Allan or Fanny and ask them about a weekly rate. They are very friendly and will work something out with you. Just tell them you are staying next door. They have rented their kayaks to people staying at Paradise so I am sure they will rent bikes. If you prefer to contact them before hand drop me a PM and I will give you Allan's email address.