The ornamental design for a beveragecontainer sling with pocket, as shown and described.
FIG. 1 is a perspective view of a beverage container sling with pocket;
FIG. 2 is a perspective view of the beverage container sling with pocket, shown with environment;
FIG. 3 is a front view of FIG. 1;
FIG. 4 is a rear view thereof;
FIG. 5 is a left side view thereof;
FIG. 6 is a right side view thereof;
FIG. 7 is a top view thereof; and,
FIG. 8 is a bottom view thereof.
The broken lines shown are included only for the purpose of illustrating unclaimed portions of the article as well as environmental subject matter, and form no part of the claimed design. Additionally, the appearance of any portion of the article between the break lines forms no part of the claimed design.