Here’s one candidate pair:
http://www.retrosheet.org/boxesetc/B06040TOR1986.htm
http://www.retrosheet.org/boxesetc/B06040ATL1986.htm
Jeff Reed finished his career with 61 homers; Bonds has 723 to date.
Total = 784 in the regular season.
So it would have to be two of the other 45 players with 392 career home runs (Carlos Delgado joined that list this year), or just one from that list and with whatever degree of help from another player.
From a check of Retrosheet it’s not Sosa, McGwire, Palmeiro, Reggie Jackson*, Mike Schmidt*, Ken Griffey Jr.*, McCovey+, Eddie Murray*, Stargell+, Winfield+, Bagwell*, Sheffield, Frank Thomas, Dave Kingman+, Andre Dawson, Manny Ramirez*, Ripken*, Alex Rodriguez, Billy Williams+, Dale Murphy, Mike Piazza nor Joe Carter.
No one else hit their first homer of the season (*or another player hit a first of the year but verified not first of career) in conjunction with those players. +And subject to the limits of Retrosheet data.)
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Of the known double-firsts, here are career totals:
http://www.retrosheet.org/boxesetc/B09090OAK1985.htm
http://www.retrosheet.org/boxesetc/B09090HOU1985.htm
Jose Canseco (462) and Matt Nokes (136) = 588 total
http://www.retrosheet.org/boxesetc/B04170TOR1987.htm
http://www.retrosheet.org/boxesetc/B04170CIN1987.htm
Fred McGriff (493) and Kurt Stillwell (34) = 527 total
http://www.retrosheet.org/boxesetc/B05290SLN1971.htm
http://www.retrosheet.org/boxesetc/B05290PIT1971.htm
Darrell Evans (414) and Milt May (77) = 491 total
http://www.retrosheet.org/boxesetc/B10040NYA1991.htm
http://www.retrosheet.org/boxesetc/B10040SDN1991.htm
Jim Thome (430 through 2005) and Tom Browning (2) = 432 total
Jim Thome (446 through 9 Aug 2006) and Tom Browning (2) = 466 total
http://www.retrosheet.org/boxesetc/B09180TEX1989.htm
http://www.retrosheet.org/boxesetc/B09180CHN1989.htm
Juan Gonzalez (434) and Mitch Williams (1) = 435 total
http://www.retrosheet.org/boxesetc/B09210SLN1985.htm
http://www.retrosheet.org/boxesetc/B09210NYN1985.htm
Andres Galarraga (399) and Dwight Gooden (1) = 400 total
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Weirdness:
Pitcher Bob Gibson hit his next to last career HR on the same day Dave Winfield hit his first.
Eric Davis hit his first of 9 homers as a Tiger (’93-’94) on the same day Manny Ramirez hit the first of his career. It was Davis’s debut for Detroit after coming over from L.A. (Brett Butler filled the power void by hitting his only home run of the year for the Hated Dodgers on that same day); Ramirez went deep twice on the day.
Dale Murphy homered twice on the day, hitting the game-winner off Rollie Fingers in the 10th and a 7th inning shot off Randy Jones that started the Braves comeback from a six run deficit. (http://www.retrosheet.org/boxesetc/B09150SDN1977.htm) This was also the date of the infamous Orioles forfeit to the Blue Jays. (http://www.retrosheet.org/boxesetc/B09150TOR1977.htm and http://www.retrosheet.org/forfeits.htm)