Can I extend my visa-exempt entry in Thailand from 30 to 60 days, and what are the requirements for proof of onward travel?

With proof of onward travel 59 days out from the date you arrive you'll be fine "ticking the boxes" and meeting the requirements from both the air carrier and the immigration people at check in.

You don't need to have another onward travel proof at 30 days

Play safe and have a ticket booked within your 30 days exemption.

The experts here know more. But there is two points that can deny you. The flight will not let you check in. Most I heard of know that you can apply for an extension and accept a ticket out after 60 day. But some gets refused.

In Thailand, immigration give you an admitted to stamp with 30 days, not 60.

Rules they follow if they check your flight is flight out of Thailand within the date he stamp. He know that you can apply for an 30 day extension of stay too. But still, it is not within the day he admit you to stay.

So, up to you. Rules is what they is. You might pass both check In and immigration. But you also might be refused already in the check in.

Note that they count your arrival day as "day 1," so make sure you are counting your days correctly. Agree that you should not cut it too close--what if your flight is cancelled or you don't make it for some reason? As you will already have an extension your options for contingency are pretty limited.

Play safe, I always leave a day before my 30 day Visa Exempt Entry permit stamp or the extension is due.