I know I'm not the only one who's been either muting the game whenever babies start crying or just aging them up as quickly as possible. Here's a mod to finally silence those screaming babies so we can play in peace!
There are separate downloads for newborns and infants - you can use them separately or together.

Choose no more than one of the following versions for newborns:
No Sounds will play the regular crying animation with the sound removed.
No Sounds Or Animations plays the happy newborn idle animations instead of the crying one, and the regular happy idle sounds will play too. The title just refers to the lack of crying sounds, and helps make it clearer that both newborn versions don't need to be installed together.

Choose no more than one of the following versions for infants:
No Sounds removes the crying infant sounds from all animations in which they occur.
No Looping Sounds only removes the sounds from looping animations, which is where I find the noise can become particularly repetitive and grating.

With any of these files, all other behaviour related to crying babies remains intact - sims will still react to the noise, etc. The baby's portrait background will also still turn blue so you can see when they need attention.

Overrides:

Newborns No Sounds
Object State Tuning 0000000000003AC4 Baby_Crying
Object State Tuning 0000000000003AC6 Baby_Happy

Newborns No Sounds Or Animations
Animation Tuning 0000000000002C00 Bassinet_baby_cry

Infants

Clip 73DA574DCD0FBED4 a2i_changingStationWall_changeDiaper_crying_y
Clip DC90C3F123031289 a2i_playmat_soc_friendly_T_tummyTimeTogether_cry_loop01_infant_y
Clip BDC13EA490429D58 a2i_playmat_soc_friendly_T_tummyTimeTogether_cry_loop02_infant_y
Clip 0FE11797004A5D92 a2i_playmat_soc_friendly_T_tummyTimeTogether_cry_start_infant_y
Clip 66F2AFD16DE7D5BD a2i_playmat_soc_friendly_T_tummyTimeTogether_cry_stop_02_infant_y
Clip C9FA35D074FB7268 a2i_playmat_soc_friendly_T_tummyTimeTogether_cry_stop_infant_y
Clip 15BB1D5D0B739170 a2i_playmat_soc_friendly_T_tummyTimeTogether_RollsCryingInfantOver_y
Clip DB2BFB83EE2DEA65 a2i_soc_friendly_T_practiceCrawling_cry_loop01_infant_y
Clip 0B674D83B8FA0064 a2i_soc_friendly_T_practiceCrawling_cry_loop02_infant_y
Clip 01CEC137EB94AECE a2i_soc_friendly_T_practiceCrawling_cry_start_infant_y
Clip 2174D2E79048025C a2i_soc_friendly_T_practiceCrawling_cry_stop_infant_y
Clip B9DA211A13C47BD4 a2i_soc_friendly_T_practiceCrawling_RollsCryingInfantOver_y
Clip 098DFF47F8B368FE a2i_soc_friendly_T_tummyTimeTogether_cry_loop01_infant_y
Clip 77D5C11D8F7C94F3 a2i_soc_friendly_T_tummyTimeTogether_cry_loop02_infant_y
Clip 41153F5F6ED4A147 a2i_soc_friendly_T_tummyTimeTogether_cry_start_infant_y
Clip C1665ECDDF0A7838 a2i_soc_friendly_T_tummyTimeTogether_cry_stop_02_infant_y
Clip 6F329529180E9503 a2i_soc_friendly_T_tummyTimeTogether_cry_stop_infant_y
Clip 92427758F625CA43 a2i_soc_friendly_T_tummyTimeTogether_RollsCryingInfantOver_y
Clip 633F29DFCA8CBBEF i_motive_cry_loop_01_layOnBack_x
Clip 8E4F6EAC64DF6237 i_motive_cry_loop_01_seated_x
Clip 87B11A691B1E6644 i_motive_cry_loop_01_seatedHighChair_x
Clip 0A71D84F8F648620 i_motive_cry_loop_02_layOnBack_x
Clip B8EA1E0579DF5FB6 i_motive_cry_loop_02_seated_x
Clip 28E4C87AA6B503EF i_motive_cry_loop_02_seatedHighChair_x
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Clip 714DEBAC060DDBAD i_motive_cry_loop_carried_x
Clip B186BCA190730325 i_motive_cry_loop02_carried_back_x
Clip 804332C6365737DF i_motive_cry_loop02_carried_x
Clip 7A7CF62041E44D2F i_motive_cry_start_carried_back_x
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Clip 50FBEE5F73637AF3 i_motive_cry_start_layOnBack_x
Clip D4BB11F51D7EDFBB i_motive_cry_start_seated_x
Clip 167F4280B6F4F9D8 i_motive_cry_start_seatedHighChair_x
Clip EB2C3014D534AADD i_motive_cry_stop_carried_back_x
Clip 33DE4B2666810E27 i_motive_cry_stop_carried_x
Clip CF6CBFCEF743A105 i_motive_cry_stop_layOnBack_x
Clip FFAA44146C61E029 i_motive_cry_stop_seated_x
Clip 02C2B2C4D5CB42F6 i_motive_cry_stop_seatedHighChair_x
Clip CDAF62FAF9B47E45 i_pullToStand_cry_loop01_x
Clip CDB9A2FAF9BD3FFA i_pullToStand_cry_loop02_x
Clip 95A4D6D4460AD618 i_pullToStand_cry_start_x
Clip C69F1957C74654B6 i_pullToStand_cry_stop_x
Clip 434CCDF48397F495 i_react_angry_cry_01_seated_x
Clip 00235DEF9B15DCD2 i_react_angry_cry_01_seatedHighChair_x
Clip 4033AB0904F86C4C i_react_sad_cry_01_layOnBack_x
Clip 5689331009D09C62 i_react_sad_cry_01_seated_x
Clip DDEA100B80CB7F5B i_react_sad_cry_01_seatedHighChair_x
Clip E8177904483D319B i_react_sad_cry_02_layOnBack_x
Clip 70A70012B95B3623 i_react_sad_cry_02_seated_x
Clip 6B117FCAF9C29EE0 i_react_sad_cry_02_seatedHighChair_x
Clip C4FBCD33B1937386 i_tummyTime_cry_loop01_x
Clip C4F20D33B18B8C41 i_tummyTime_cry_loop02_x
Clip 7FC78DCC18BB7675 i_tummyTime_cry_start_x
Clip 3704FE07735A5E6C i_tummyTime_cry_stop_02_x
Clip B99638B6320D30B9 i_tummyTime_cry_stop_x
Clip 8C1622AD88FC7097 i2o_crib_pullToStand_cry_loop01_x
Clip 8C1222AD88F88860 i2o_crib_pullToStand_cry_loop02_x
Clip A897EEA80E59E8A6 i2o_crib_pullToStand_cry_start_x
Clip 309AA221073725D0 i2o_crib_pullToStand_cry_stop_x

No More Crying Babies