You really don't. The airlines have been moving away from classifying discounted first class fares as Y-UPs, as it was leading to all sorts of problems when passengers were downgraded.
In any event, the lowest available Y-UP fare, while technically an economy fare, is still meaningfully more expensive than the lowest available coach fare; most corporate travel policies would require the lowest available fare, unless you have the ability to purchase refundable fares, then maybe you would have more flexibility.

In any event, you can purchase the coach fare through the travel agent, and then you *should* be able to call AA and "up-fare" the ticket to first class by only paying the fare difference.

Alternatively, some companies/travel agents will let you purchase the more expensive first class fare, but will document what the lowest coach fare was and only reimburse that amount. Talk to your travel agent or corporate travel department (and probably your accounts payable people as well who process expense reports!).