Two ideas:

(1) Treat your coins as particles with position and velocity, and place them under the influence of a strong attracting force towards the player.

(2) Create two trajectories for each coin: one that goes away from the original location in some random direction, and one that goes from the original location to the location of the player. At each step, compute the location of the coin under both trajectories and interpolate between them linear interpolation, where the weight of the first trajectory in the interpolation starts at 1 and goes to 0 following some curve (perhaps something like weight_of_the_first_trajectory = 1 - (time/transition_time)^2).