If you want to keep close to the sentences suggested in the question, then this one could be salvaged:
Прошу вас оформить этот товар двумя частями
"Двумя частями" is a good expression, somewhat frequently used in newspapers and magazines, see real examples (highlighted orange) in these corpus search results.
But you should carefully choose the verb so that it would be clear that you want the payment to come in two parts, not the product.
- Прошу вас принять оплату за товар двумя частями.
- Я бы хотел оплатить товар двумя частями.
- Мне было бы удобно перечислить полную сумму двумя частями.
All three examples above would work with "двумя платежами" too. On one hand "двумя платежами" is less ambiguous since it's already about the payment. On the other hand it would repeat the same root twice in a sentence (оплата-платежами), which might be considered a less-than-perfect style.
Alas, the second suggested sentence, "в две рассрочки" is impossible. "Рассрочка" already means the process of paying the debt in chunks. "Две рассрочки" implies that you're asking for two installemnt plans, rather than for two installemnts.
Another good translation for "installment" is "взнос". It's formal enough and can be used in legal documents, particulary in insurance premium installemnt plans.
- Прошу вас разбить оплату на два взноса.
- Мне хотелось бы оплатить товар в рассрочку двумя взносами.