Kelly, many of the more mature nannies out there will have experience caring for young babies.
Certainly as a babysitter myself I have cared for many babies aged from 3-days old upwards, including twins. (I won't post my website, I'm sure anyone that interested can easily find it - just search Google!)
Personally I would avoid using an agency, as most agencies will not be able to guarentee you the same person to babysit. With babies you want to try and have consistancy of care, so your children don't mind you going out, so that the carer knows your children, knows your home and any pets, knows the routines etc. You don't really want to have someone new everytime you fancy a few hours out with DP without the children in tow.
You also want to leave your home happy that your children will be well cared for, you can hardly do that if you've just spent 5 minutes getting to know a sitter who has just arrived for the night who you may never see again.
Try the shop window approach, aiming at nannies who may be working in your area... you may strike lucky. Also use NannyJob and search Google for childcare providers in your area who do the odd bit of evening work.
Kid - I find twins easier than singletons. Currently babysit for two sets of twins - both are a pleasure to babysit for.
Kelly wrote>I get the dts off to sleep by takign them thru to our bedroom, swaddling them, and giving them a bottle in semi-darkness, then putitng them in their cots. Can I ask the sitter to do that?
Kelly, it's something I do when I babysit for families with a baby. I stick with whatever routine is already in place, children feel far more secure that way. Dab hand at bottle feeding in darkness!
Good luck in whatever you decide... hope you find a suitable babysitter soon.