The short answer is, No!
And if you ever kill animals/ birds thinking the ‘sacrifice’ will help you, you are in for a traumatic time. If you ever kill any living being, thinking that this ‘sacrifice’ will take away your problems or give you happiness, you will create horrible karma for yourself. Such killing is not allowed, ever. This is applicable to everyone irrespective of the faith he follows.
बलि Bali is a Sanskrit word and has several meanings like levy, offering, oblation, revenue due to the king, tribute, worship, gift, offering, power, strength, might, karma etc. There was King of the Asuras named Maha-Bali who was extremely wise, strong, generous etc. The root word is Bala बल which essentially means strength. When you give ‘Bali’ you are essentially powering your intention with this act of Bali. In Sanantan Dharma, if someone says that you should give Bali, it means that you have to offer a coconut. Only this one item, नारिकेल coconut, is Bali. Nothing else is acceptable as Bali, ever.
You go to any temple in India, or at the ghats/ banks of sacred rivers, you will find that the flower vendors there always have the coconut as a part of the puja flowers set-up on sale. When you go inside the temple, you will offer this, coconut, flowers, sweets, kumkum, turmeric, akshata, camphor, incense sticks etc to the deity with your prayers/ intention. The priest will generally break open the coconut and give you half of it as a prasadam. Or he will touch the coconut to the deity’s feet and give it back to you, you are now expected to break it at a designated place inside the temple. This one fruit has the capacity to amplify your intention, to add power to your wish and will help in getting it fulfilled soon. You can offer a coconut /Bali in a temple or in your home puja-ghar or at sacred rivers/ sea etc. Bali is also performed when you start something new for the first time or when you need added protection or an added boost of power. eg when entering a new house, or entering your new office, when driving a new car for the first time, etc. All auspicious activities are powered by a Bali of the coconut.
A brief procedure would be this.
You take a brown coconut which has water in it. This water part is necessary, so do check if you can hear the water sloshing inside the coconut. Then remove the excess fibres on it leaving a tuft at the point where its ‘eyes’ are. If you do not remove these fibres, breaking it with a single dash will be difficult. Stand in front of your deity. Keep the coconut in front of it. Pray for whatever it is that you want from the deity. Or wish for general happiness and prosperity. You can use Sanskrit mantra-s if you know them or speak in the language you are comfortable in. Just keep your mind clear and intention strong. Then apply Kum-kum, turmeric, unbroken raw rice/ Akshata, flowers etc, if you have these items, to the deity and to the coconut. Then hold the coconut in your hand. Express your wish again intensely in your mind. Then dash this coconut on the ground before the deity so that it breaks. It must compulsorily break in one dash. If it does not break then it is considered inauspicious. This requires strength, so this part is generally done by the men, father/ brother/ husband/ son or the pujari in the temple will do it. The water from the coconut will spill as it gets broken, if you can catch it in your palm, you can drink it as a teerth. Afterwards you can eat the coconut white as a prasadam.
A coconut is a scared object but obviously it is also used in the kitchen. Like I use 1-2 coconuts in my kitchen in an average week. But even if I am going to use it in a chutney or a curry, when it is being broken, my husband will say aloud the name of the family deity and break it cleanly in a single dash.
There are some videos where animals/ birds are being shown killed in the name of deities, especially Ugra-roop of deities, often Devi Kali. This does not feel right in the energy sense. I was watching a weird ritual on Youtube where Her Moorti was drenched with the blood of these killed animals. The blast of negativity from the scene was unbelievable. So then I asked the Devi Kali Herself about this (even you can ask deities questions and they always answer). She clearly said that if you cannot give it life you cannot take its life. The energies of the animals/ birds who are killed are absorbed by Her Gana-s and not by Her. The Gana-s are the attendants of the deities and are capable of granting minor blessing, siddhi etc etc on their own. If you get caught in these minor things from the Gana-s you will never be able to focus on Her. This is a traumatic death of a living being, the energies are inauspicious so are more used for the maran, maaran, vidveshan etc types of prayog. This is a tamasic activity which cannot add auspiciousness. But people who do not know better indulge in this as it does give results. The energy of physical death is a powerful force which can be used for hurting others. But it is a power born of trauma and will eventually give only trauma. It always turns back on the practitioners themselves. Regular people like you and me should never get into these types of prayogs, they will turn on you later and give spectacularly horrid results.
In some cultures all over the world, mass killing of animals as ‘sacrifices’ is practiced routinely. This energy of traumatic death increases the negativity of these people and the place too. In fact it feeds the energies of dissonance, discordance and strife in the subtle planes around the Earth. And obviously create negative karma for those doing it.
So if you feel that you have to do a Bali, go ahead, dash a coconut and power your intention, it will always help. But never ever harm an animal/ bird thinking that its death will help you gain your desire. This is short term gain for long term pain.