Most commemorative coin bills of the classic era were introduced, considered/debated and passed in the same session of Congress (sometimes across two sessions of the same Congress). There were instances, however, of a coin proposal being considered across two distinct Congresses.
This post takes a quick look at them.
1936 Norfolk, VA Bicentennial/TricentennialIntroduced: 74th Congress, 2nd Session
Amended & Approved: 74th Congress, 2nd Session
Re-Introduced: 75th Congress, 1st Session
Re-Approved: 75th Congress, 1st Session
The commemorative piece for the 300th Anniversary of the Norfolk land grant and 200th Anniversary of the establishment of Norfolk, VA as a borough, was introduced in the 74th Congress via House and Senate companion bills as a 50-cent coin. As the bill was being considered by Congress, it was amended in the Senate to specify a medal vs. a coin. The bill was approved and it appeared as if Norfolk's anniversaries would be celebrated via a US Mint-struck commemorative medal. When the 75th Congress convened, however, it approved several commemorative coin bills. This caused the Norfolk sponsor to reconsider its acceptance of a medal and it restarted its push for a 50-cent coin. It was successful in its efforts, and secured the half dollar collectors are familiar with today.

For more of the Norfolk medal vs. coin story, see:
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1936 Norfolk Bicentennial / Tricentennial - Medal Vs. Coin1937 Battle of Antietam 75th Anniversary Half DollarIntroduced: 74th Congress, 2nd Session
Approved: 75th Congress, 1st Session
A coinage bill for the Battle of Antietam 75th Anniversary was introduced during the Second Session of the 74th Congress and was ready to be authorized in its waning days, but, due to an apparent clerical error, was not brought up for a final vote in the House before it adjourned. As a result, the bill died and needed to be re-introduced in order for the Antietam half dollar to become a reality. A new Antietam bill was subsequently introduced at the opening of the 75th Congress and was soon passed.

For more of the Antietam story, see:
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1937 Battle Of Antietam 75th Anniversary - RevisitedFor other posts about the Norfolk and Antietam half dollars, as well as other of my posts about commemorative coins and medals, check out:
Commems Collection..