How can I convert my 60-day tourist visa into a re-entry permit in Thailand?

As long as you realize that a re-entry permit will NOT add any more time to your original 60 day stamp you can get a re-entry permit at the immigration office OR at Suvarnabhumi or Don Mueang Airports before you fly out.

you have to do the count by yourself to find out if buying a re-entry permit for 1000 THB is worth while. Did you understand what James wrote? The admitted-to-stay date will remain the same on re-entry, as it was given to you when you entered Thailand on this Single Entry Tourist Visa. In case there are less than 30 days left until your admitted-until date on the date you plan to travel out of Thailand, you don't win one single extra day with a re-entry permit . . . . you can get the a 30 day visa exempt as a citizen of Czech Republic upon re-entering Thailand for free . . . . . and you will be able to extend this one by 30 more days on any immigration inside Thailand for 1900 THB (the same fee which applies if you would extend a 60 day tourist visa for 30 more days!) You are free to both options . . count your planned days of stay and travel carefully . .

If you have days left on your Admitted to Stay period and planning to leave Thailand and come back before the Admitted until ../../.. date stamped in your passport you can apply for the Re-Entry Permit and get the same Admitted until date stamped in your passport on return.

Then just do as

@Robert ******

said...get a reentry permit from Thai Immigration before you leave.

Or are you just wanting to extend your stay in Thailand for 30 days?

Are you wanting to leave and reenter Thailand? For what purpose? To have added 30 days in Thailand? Or to visit another country?

If you have days left on your Admitted to Stay period and planning to leave Thailand and come back before the Admitted until ../../.. date stamped in your passport you can apply for the Re-Entry Permit and get the same Admitted until date stamped in your passport on return.