Ms. Bautista’s lawyer, Fran Hoffinger, said the court should impose no jail sentence because of Ms. Bautista’s frail health. She pointed out that paramedics had wheeled Ms. Bautista out of the courtroom on a gurney twice during her five-week trial after heart palpitations and fainting spells.

“Incarceration for her would be a death sentence, or at least a life sentence,” Ms. Hoffinger said.

A jury took less than three hours to convict Ms. Bautista in mid-November of conspiracy and tax fraud in connection with the sale of the Monet piece, “Le Bassin aux Nymphéas” (1899). The painting ended up in the hands of the financier Alan Howard after a complex $43 million transaction in September 2010, involving the Hazlitt, Gooden & Fox Gallery in London and a Panamanian shell company.

The painting had been taken along with three other valuable works in late 1995 from the walls of an Upper East Side townhouse, owned by the Philippine government, where Mrs. Marcos stayed and held lavish parties when in New York. Ms. Bautista maintained she had Mrs. Marcos’s written permission to sell the works, which were found in Ms. Bautista’s apartment in Manhattan. The Philippine government is seeking to recover them.

The jury found Ms. Bautista guilty of conspiracy for having plotted with her two nephews, Chaiyot Jansen Navalaksana and Pongsak Navalaksana, to sell the four paintings on the Asian black market. Eventually they succeeded in finding in Mr. Howard a final buyer for the water lily canvas. Along the way, they enlisted the help of Ms. Bautista’s Philippine lawyer, two New York real estate agents, an agent in Europe and the dealers at the London gallery. The nephews remain fugitives abroad.

Ms. Hoffinger said the appeal would challenge, among other things, the judge’s decision to let into evidence reams of emails between Ms. Bautista’s nephews that the prosecution used to prove the conspiracy. The defense argued that the correspondence should not be admitted because Ms. Bautista did not write them and they were not properly authenticated.