It's easy to hire bikes. If you enter the park from the Paddington Gate, then you'll see the hire station on the left just after you turn onto Grand Drive.
As well as regular bikes they also hire out 4 wheel cycle buggies which are a lot of fun, although they no longer hire out rollerblades.
There are various places near the park which hire out rollerblades and the safety gear including Skater HQ which is situated in the nearby Moore Park Entertainment Quarter. It will cost you about $25 for 2 hours.
Centennial Park is a great place to learn to rollerblade and you won't be the only one teetering around and crash landing on the grass.
However rollerblading takes some practice and most people will have a much more enjoyable experience (and you'll be much less likely to injure yourself) if you get some lessons first. A good place to start is Rollerblading Sydney where James can provide you with lessons, equipment hire, and advice on which gear will be most suited to you.
There are lots of great spots for a picnic in Centennial Park, just drive or walk around until you find somewhere you fancy. There are also public BBQs scattered here and there and a very nice cafe/restaurant as well.
You can usually find a park in Centennial park itself without too many problems, and Oxford St is well served by buses.
If you are going on a Saturday you could go shopping in the morning on Oxford St and at the Paddington Markets, then grab some food from a deli (or the markets), wander down to the park and eat, sleep it off on the grass, and then go for a cycle or rollerblade. Makes for a great day.
Why? Fresh air, exercise, fun, another excuse for a picnic.