If this was a direct PAL itinerary (US-Cebu via Manila), you may not be running into this problem, and you can get a quotation easily on PR and pay for it as well. However, since you have made note that you're flying DL into Manila, it may get a little trickier. The websites of Philippine airlines (PAL and Cebu Pacific had their fair share of problems with foreign credit cards) are not always the best with respect to foreign cards, though people have tried and gotten their transactions through without a sweat in certain instances.
I can give three suggestions:
*You can call PAL and make a reservation for MNL-CEB. Depending on the fare class, reservations can last for as long as one week, if memory serves me right, or even longer. When you arrive in Manila, you can pay for and claim your MNL-CEB ticket at any PAL ticket office: if you're flying to Cebu the next day, there's a ticket office at NAIA-2. I'm not sure though if this will work, but you may also be able to pay at the PAL ticket office in your area, if you're near one.
*You can use a third-party website, like Expedia. Travel websites usually have domestic PAL flights in their inventory, though not all websites do: for example, Travelocity doesn't allow bookings from the Philippines, but their affiliate Zuji does (prices quoted in Singapore dollars).
*You can standby for MNL-CEB.
Just a fair warning: because you're flying Delta into Manila and purchasing a PAL ticket separately, your baggage allowance does not carry over to your PAL flight. Again, depending on the fare class, your baggage allowance can either be 15 or 20 kilograms in Fiesta Class and 30 kilograms in Mabuhay Class. Any amount over the limit will warrant baggage fees, though some counter agents are lenient with bags, particularly if the flight is not full. This is more likely to happen if your flight is on a widebody (A330, 744 or 77W) than on a narrowbody (A320, sometimes A319).
Hopefully you enjoy your PAL flight.
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Update for people who visit the PAL website: you can now choose your seat while booking! ^