After age 59.5, can I make an IRA contribution, and a withdrawal in the same year?

Sure. But you need to figure out whether you want the withdrawal to actually be a return of your contribution (which you are allowed to do in the same year as your contributon), or an actual withdrawal that includes a partial return of your after-tax contributions plus pre-tax contributions and earnings in the account. If your contribution was with after-tax money you are better off having the contribution returned rather than traking an actual withdrawal. If the contribution was using pre-tax money (tax-deductible) then you're slightly better off taking a distribiution rather than a return of the contribution. Talk to the IRA custodian and see if they give you a choice on how you handle this.