Dora Bas Rivka Silver O'H
Just to be on the safe side…
If the two birds pose a financial hardship, the person could bring a flour offering. Because it's being brought as a sin offering, it would not have oil or frankincense placed on it.
Me'ilah is when someone took an item consecrated for use in the Temple (or the Tabernacle) and made personal use of it. If someone did this by accident, he would have to bring a ram for a guilt offering. He would also have to replace whatever he used, adding one-fifth.
Another type of guilt offering was the asham talui, or "conditional guilt offering." This sacrifice was brought when a person wasn't sure if he violated certain laws (the kind that carry the penalty of kareis - excision - if committed intentionally). The asham talui was a ram offered "just in case."
A person sins not only against another person but also against G-d when he acquires property dishonestly, no matter how it came into his possession. Whether a person steals something outright, cheats another in business, refuses to return an object he was watching or denied finding a lost item, he must return the property to its rightful owner and add one-fifth to it. Then, he should bring a ram as a guilt offering.
In case you ever fretted about one's inability to fulfill every mitzvah in the Torah, returning a misappropriated object is a mitzvah one can't fulfill without first acquiring something illegally. Some mitzvos are better off not being necessary.