One alternative might be to say, next time she asks about a play date, "Let's have it at the playground." And ensure no one brings their own toys there. The other boy will have less "ammo" to throw at/take from your son; no one can "own" a slide or the monkey bars; and it's possible that the larger space and the chance to run will help this boy burn off some of what seems to be his excess energy and aggression. Of course you will have to take care that the boy does not pick up sticks etc., or push or shove while on top of a slide for instance; I would monitor them both pretty closely at a first playdate at a park (maybe standing at the slide to enforce a "one at a time on top" rule) etc. The boy's behavior at a park could be much "better" in the sense he might be occupied enough not to hit; or it could be worse if he thinks he owns the place (which many kids his age do!). It's just something to try, perhaps.
Someone posted that this is normal, 3-year-old, hard-time-sharing behavior, and I agree that mostly that's right, but if this child is hitting your child every single time and you are finding every single playdate to be this stressful -- you are right to avoid play dates with this boy for now. If you don't want to try the playground experiment, you could just tell the mom, "I know (son) and (boy) like to play together, but they don't seem to be able to share well just yet. Let's revisit the idea later in the summer." That gives you the option of being able to call her in a few months and try again. And if you consider her a friend -- be sure to invite her out for coffee sometime when all the kids are otherwise occupied, to keep that adult connection.
It's entirely possible that this boy will outgrow this behavior soon -- around three to three and a half is a tough age, and then at four many kids deal better with sharing and not touching. But you do not have to continue play dates for now, especially if your son has other friends who do not hit and who find sharing a little easier.
Meanwhile, are you getting other play dates with other kids? That is a legitimate reason to say, we're busy!