I only have 1-2 "close" friends too. I have a lot of other people I consider friends, mostly from my daughter's schoolmates. I too am not very close, personally or locationwise, to immediate family. Very few of our neighbors have kids my kids' ages, so we're stuck there too.
I "decided" that I would let my daughter tell me who her best friends were, then I ask her questions over time about those kids, to see if they have similar interests to her and such. Then I work to make friends with those kids' parents, invite them over for playdates, give the other parent a "break" on 1/2 days of school and we go to the movies or do something really fun. I try to make our house "the cool house" to be at, so the kids think to call us when they have time to play. I don't "seek" return playdates, but it usually just happens. I also casually say things like, "What are you guys up to for the winter break" when the parents come to pick up, or I see them at school.
Finally, we do some extra cirriculars like gymnastics and scouts too. That has really helped forge some bonds between small groups of kids and us parents. Once again, I offer to drive, have the kids over to play, etc.
I found that by making friends with the parents of these kids, we already have some common bonds/interests. That helps secure a friendship. Plus, many of us continue classes/scouts for a long time to come so it's usually familiar faces over time.
We talk MOST often at drop off/pick up times when we're waiting for the kids. It's easy to make friends with other people you know you're already going to see time and time again instead of trying to get together with people you wouldn't normally see on a regular basis. Proximity and school schedules help.
I would keep "inviting" your cousins to "join you" at the zoo, park, etc. but don't expect their company. Perhaps you can "invite" them to join you and your kids at a winter break outing like at a pottery place or something where you KNOW the kids will have fun? I know we feel a little isolated when winter's here. So having somewhere to go, to have some fun might work for you - esp if you're OFFERING for them to drop off their kids so they can "Christmas shop" or have a couple of hours to themselves.
Best wishes.