In section 9.1 on page 69 of the PIC16F877 data sheet, the text before the last bulleted list says "For the pins to behave as the serial port function, some must have their data direction bits (in the TRIS register) appropriately programmed" and the second bullet point says "SDO must have TRISC<5> cleared". This implies that you can control whether the RC5/SDO pin is an output or not using TRISC bit 5.
If that's the case, you can set the RC5/SDO pin (SDO aka MOSI) to input mode by setting bit 5 of TRISC, without affecting the SPI peripheral. This means you should be able to connect the SDO/MOSI and SDI/MISO pins together. When you're transmitting a byte, clear TRISC bit 5; when you're receiving, set TRISC bit 5.
However, Figure 3-5 on page 33 shows that the output enable control of RC5 is controlled by the output of the TRIS latch ORed with a signal called "Peripheral OE". This implies that the peripheral can force the pin to output mode, although it doesn't say where the "Peripheral OE" signal comes from for RC5.
You might have to ask Microchip technical support if you need an answer on whether RC5/SDO can be put into input mode using TRISC bit 5 without disrupting the SPI peripheral.
In any case you'll need to check the exact timing and phase of the clock and data signals used by both the PIC and the accelerometer to make sure that everything happens when it's supposed to. gorgon mentions the need for a dummy bit in the command byte. I haven't looked into this, but you need to.
I think you also have to enable SPI 3-wire mode by setting the SPI3W bit, bit 5, in the Mode control register (register 0x16) before you can do any other communication with the device. This is mentioned in item 2 in the Quick Start guide on the last page of the module documentation.