Yes, you can make the nondeductible IRA contribution by investing the $2,000 per year. Please note you must file Form 8606 with your tax return to let the IRS know that contribution was nondeductible. Also, this form informs the IRS your contribution was "after tax" and they cannot tax it again. One more thing, if you do not file Form 8606 with your return, the IRS will impose a penalty of $50 per year for failure to filing the form.

PS- It may be a good idea to show your family and beneficiaries the Form 8606 and tell them to make sure the IRS doesn't tax you again on the withdrawal. IRS may try to pull a double whammy on you... death and taxes at the same time.