I think you'll find that for 1-2 days a week you'll have a hard time finding a spot for an infant in a daycare center, although it's worth a shot to look around. So, that basically leaves you with home daycares and nannies. You might look into sharring a nanny with another family, as that tends to be a bit more affordable than hiring a nanny on your own.
For in home daycares, I would contact West Suburban Home Day Care Association at ###-###-####. They can provide you with a list of providers that currently have openings. While most providers have plenty of experience with new babies, I personally would look for a provider that currently has a younger crowd as opposed to a houseful of toddlers and pre-schoolers. Just my preference...
One home daycare that I visited and really loved was Annie Forde at ###-###-#### just north of OP in Galewood. She's an Irish mom of 5 kids! She may or may not have openings and likely has a group of older children, but she seemed so nurturing that I would not hesitate to leave my baby with her despite an older group of kids.
Best of luck!