There were no lists of passengers leaving Liverpool, but passengers were listed as they arrived in New York.

Give them a few days in Liverpool to board the ship, and for the ship to leave port. Then expect that the sailing time Liverpool-New York was about 40 days. So they probably arrived in New York in late May. Look at the LDS films (Indexed under "New York, New York" and then "Emigration and Immigration":

"Passenger lists of vessels arriving at New York, 1820-1897; index to passenger lists of vessels arriving in New York, 1820-1846"

(I copied the ones that seem most likely.)

Passenger lists 19 Apr 1849-3 May 1849; FHL US/CAN Film 175433

Passenger lists 4 May 1849-4 Jun 1849; FHL US/CAN Film 175434

Passenger lists 5 Jun 1849-15 Jun 1849; FHL US/CAN Film 175435

Order at your nearest LDS Family History Center, for about $3.50 rental.

Good luck!