This is due to the special behavior of SetDelayed (:=) with regards to the first argument (see e.g. this question): The arguments of the l.h.s. are evaluated by SetDelayed, which causes the error you are seeing - after all, SeriesData[_, _, coeff_, _, _, _] is not a valid SeriesData construct. This is what HoldPattern is designed for: It prevents evaluation of its argument (like Hold), but is invisible to the pattern matcher. The solution is therefore simply:

(* prevent the l.h.s. from being evaluated *)
HoldPattern@getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

getCoeff@Series[E^(π x), {x, 0, 3}]
(* π *)

(* prevent only evaluation of the first argument (equivalent in this case) *)
getCoeff[HoldPattern@SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

getCoeff@Series[E^(π x), {x, 0, 3}]
(* π *)

In this case the error would be of no consequence: If you look at ?getCoeff, you'll see that the definition that was actually made is the same with and without HoldPattern. If you evaluate SeriesData[_, _, coeff_, _, _, _] on its own, you will see that you get the error message, and then the input will be returned (which happens for many Mathematica functions) - if you would have gotten something else back, the definition would not work.

This is due to the special behavior of SetDelayed (:=) with regards to the first argument (see e.g. this question): The arguments of the l.h.s. are evaluated by SetDelayed, which causes the error you are seeing - after all, SeriesData[_, _, coeff_, _, _, _] is not a valid SeriesData construct. This is what HoldPattern is designed for: It prevents evaluation of its argument (like Hold), but is invisible to the pattern matcher. The solution is therefore simply:

(* prevent the l.h.s. from being evaluated *)
HoldPattern@getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

getCoeff@Series[E^(π x), {x, 0, 3}]
(* π *)

(* prevent only evaluation of the first argument (equivalent in this case) *)
getCoeff[HoldPattern@SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

getCoeff@Series[E^(π x), {x, 0, 3}]
(* π *)

As noted in the comments, the original version works perfectly fine ignoring the error message: If you look at ?getCoeff, you'll see that the definition that was actually made is the same with and without HoldPattern. If you evaluate SeriesData[_, _, coeff_, _, _, _] on its own, you will see that you get the error message, and then the input will be returned (which happens for many Mathematica functions) - if you would have gotten something else back, the definition would not work.

This is due to the special behavior of SetDelayed (:=) with regards to the first argument (see e.g. this question): The arguments of the l.h.s. are evaluated by SetDelayed, which causes the error you are seeing - after all, SeriesData[_, _, coeff_, _, _, _] is not a valid SeriesData construct. This is what HoldPattern is designed for: It prevents evaluation of its argument (like Hold), but is invisible to the pattern matcher. The solution is therefore simply:

(* prevent the l.h.s. from being evaluated *)
HoldPattern@getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

getCoeff@Series[E^(π x), {x, 0, 3}]
(* π *)

(* prevent only evaluation of the first argument (equivalent in this case) *)
getCoeff[HoldPattern@SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

getCoeff@Series[E^(π x), {x, 0, 3}]
(* π *)

This is due to the special behavior of SetDelayed (:=) with regards to the first argument (see e.g. this question): The arguments of the l.h.s. are evaluated by SetDelayed, which causes the error you are seeing - after all, SeriesData[_, _, coeff_, _, _, _] is not a valid SeriesData construct. This is what HoldPattern is designed for: It prevents evaluation of its argument (like Hold), but is invisible to the pattern matcher. The solution is therefore simply:

(* prevent the l.h.s. from being evaluated *)
HoldPattern@getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

getCoeff@Series[E^(π x), {x, 0, 3}]
(* π *)

(* prevent only evaluation of the first argument (equivalent in this case) *)
getCoeff[HoldPattern@SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

getCoeff@Series[E^(π x), {x, 0, 3}]
(* π *)

In this case the error would be of no consequence: If you look at ?getCoeff, you'll see that the definition that was actually made is the same with and without HoldPattern. If you evaluate SeriesData[_, _, coeff_, _, _, _] on its own, you will see that you get the error message, and then the input will be returned (which happens for many Mathematica functions) - if you would have gotten something else back, the definition would not work.